*79 B.P. is a 19-year-old public school student in Regional School Unit 75 (the "district") in Topsham, Maine. He has been diagnosed with several disabilities, including autism, cognitive impairment, and a variant of Landau-Kleffner Syndrome. B.P. is nonverbal and unable to communicate with his parents about his experiences at school. His parents want him to carry an audio recording device at school to record pretty much everything said in his presence. The school district's refusal to permit the device prompted B.P.'s parents ("plaintiffs") to file this lawsuit on his behalf under, among other things, the Americans with Disabilities Act ("ADA"). They also commenced an administrative proceeding under the Individuals with Disabilities Education Act ("IDEA"). As we will explain, because the administrative tribunal found that carrying the recording device would provide B.P. no demonstrable benefit, plaintiffs are precluded from proving an element necessary for them to prevail on their ADA claim. We therefore affirm the judgment for the district.

I.

We begin by describing the basic framework of the two principal statutes at issue in this case: the IDEA, under which the plaintiffs' administrative claim was adjudicated, and the ADA, under which the claim relevant to this appeal arises. 1

A.

The purpose of the IDEA is "to ensure that all children with disabilities have available to them a free appropriate public education that emphasizes special education and related services designed to meet their unique needs." 20 U.S.C. § 1400 (d)(1)(A). A free appropriate public education, commonly referred to as a FAPE, is defined to include "special education and related services that ... are provided in conformity with [a student's] individualized education program." Id. § 1401(9)(D). "Special education" is further defined as "specially designed instruction ... to meet the unique needs of a child with a disability." Id. § 1401(29). "Related services" include supportive services, such as audiology and interpreting services, "as may be required to assist a child with a disability to benefit from special education." Id. § 1401(26)(A). "Supplementary aids and services" can also be included in a student's individualized education program ("IEP"), see id. § 1414(d)(1)(A)(i)(IV), and are defined as "aids, services, and other supports that are provided in regular education classes ... to enable children with disabilities to be educated with nondisabled children to the maximum extent appropriate," id. § 1401(33).

If parents are concerned that their child is not receiving a FAPE, they can file a complaint with the local educational agency. See id. § 1415(b)(6)(A). The agency then has the opportunity to resolve the complaint at a preliminary meeting with the parents and the relevant members of the IEP team. See id. § 1415(f)(1)(B)(i). If that meeting fails to resolve the complaint "to the satisfaction of the parents" within a *80 certain time period, id. § 1415(f)(1)(B)(ii), the parents are entitled to have the issue decided in an impartial due process hearing, see id. § 1415(f)(1)(A). There are two types of arguments available to the parents at a due process hearing, both of which center on the denial of a FAPE. They can argue that their child is being denied a FAPE substantively, on the grounds that his or her IEP lacks certain special education or related services. See id. § 1415(f)(3)(E)(i). And they can argue that their child is being denied a FAPE due to procedural violations that, for example, "significantly impede[ ] the parents' opportunity to participate in the [IDEA] decisionmaking process." Id. § 1415(f)(3)(E)(ii)(II).

B.

Casting a much wider net than the IDEA, the ADA seeks to eliminate discrimination against all individuals with disabilities. See 42 U.S.C. § 12101 (b)(1). Title II of the statute mandates that "no qualified individual with a disability shall, by reason of such disability, be excluded from participation in or be denied the benefits of the services, programs, or activities of a public entity, or be subjected to discrimination by any such entity." 2 Id. § 12132. This protection "is characterized as a guarantee of 'meaningful access' to government benefits and programs." Theriault v. Flynn , 162 F.3d 46 , 48 (1st Cir. 1998) (quoting Alexander v. Choate , 469 U.S. 287 , 301, 105 S.Ct. 712 , 83 L.Ed.2d 661 (1985) ); see also Iverson v. City of Boston , 452 F.3d 94 , 99 (1st Cir. 2006) ("The clear purport of Title II is to guarantee that qualified disabled persons enjoy meaningful access to public services, programs, and activities.").

It is undisputed that B.P. is a qualified individual under the ADA. And for purposes of our review of the district court's summary judgment ruling, the school district does not dispute that to the extent B.P. did not obtain access to (or the benefits of) the district's services, it was by reason of his disability. Therefore, the only contested ADA issue for purposes of this appeal is whether, by rejecting plaintiffs' requests to equip B.P. with a recording device, the district denied him "the benefits of [its] services, programs, or activities" or otherwise discriminated against him.

Such an unlawful denial occurs if a public entity refuses to "make reasonable modifications ... when ... necessary to avoid discrimination on the basis of disability, unless the public entity can demonstrate that making the modifications would fundamentally alter the nature of the service, program, or activity." 28 C.F.R. § 35.130 (b)(7)(i). As noted in Nunes v. Massachusetts Department of Correction , 766 F.3d 136 (1st Cir. 2014), required modifications, or what we more customarily call "accommodations," 3 include those reasonably *81 necessary "to provide meaningful access to a public service." Id. at 145 (internal quotation marks omitted).

In considering failure-to-accommodate claims under the ADA, we are also guided by duly enacted regulations implementing the statute's anti-discrimination mandate. See A.G. v. Paradise Valley Unified Sch. Dist. No. 69 , 815 F.3d 1195 , 1204 (9th Cir. 2016). One such regulation promulgated by the Department of Justice is relevant here. The so-called effective communications regulation requires public entities "to ensure that communications with applicants, participants, members of the public, and companions with disabilities are as effective as communications with others." 28 C.F.R. § 35.160 (a)(1). To achieve this, "public entit[ies] shall furnish appropriate auxiliary aids and services where necessary to afford individuals with disabilities ... an equal opportunity to participate in, and enjoy the benefits of, a service, program, or activity of a public entity." Id. § 35.160(b)(1) ; see also K.M. ex rel. Bright v. Tustin Unified Sch. Dist. , 725 F.3d 1088 , 1102 (9th Cir. 2013) (noting that "we are guided by the specific standards of the Title II effective communications regulation" because "the 'meaningful access' standard incorporates rather than supersedes applicable interpretive regulations").

A plaintiff pursuing an accommodation-based claim of discrimination under the ADA must in the first instance make several showings, one of which is the "effectiveness" of the proposed accommodation. Reed v. LePage Bakeries, Inc. , 244 F.3d 254 , 259 (1st Cir. 2001) (explaining that the plaintiff has the burden to show that the proposed accommodation is effective and reasonable). In other words, the accommodation must provide a benefit in the form of increased access to a public service. See Nunes , 766 F.3d at 145 . Nothing in the effective communications regulation obviates the need to show that a requested accommodation will provide some such benefit. To the contrary, the regulation only requires public entities to provide auxiliary communication aids and services " where necessary to afford individuals with disabilities ... an equal opportunity to participate in, and enjoy the benefits of, [the entity's] service, program, or activity." 28 C.F.R. § 35.160 (b)(1) (emphasis added). And although the regulation directs that "[i]n determining what types of auxiliary aids and services are necessary, a public entity shall give primary consideration to the requests of individuals with disabilities," id. § 35.160(b)(2), the requested aid or service must still be beneficial in the first instance. See United States Dep'ts of Educ. and Justice, Frequently Asked Questions on Effective Communication for Students with Hearing, Vision, or Speech Disabilities in Public Elementary and Secondary Schools 8-9, https://www2.ed.gov/about/offices/list/ocr/docs/dcl-faqs-effective-communication-201411.pdf.

II.

We next recite the relevant travel of plaintiffs' multi-track pursuit of their claims under the ADA and IDEA. Plaintiffs sued the district and several school officials in March 2013, alleging violations of the First Amendment, the ADA, the Rehabilitation Act, and the IDEA. In May 2014, plaintiffs filed a second suit against the district and several other school officials, alleging that the district had "continued the pattern" of violating their rights under those statutes. The two cases were *82 consolidated in the district court and in due course the parties filed cross-motions for summary judgment.

The district argued that plaintiffs had failed to exhaust their administrative remedies under the IDEA, which barred their claims under the First Amendment, the ADA, and the Rehabilitation Act. In response, while the parties were awaiting a decision on the summary judgment motions, plaintiffs began the process of exhausting their IDEA remedies by requesting a due process hearing from the Maine Department of Education in early January 2016. 4 In that request, plaintiffs asserted numerous violations of the IDEA and sought, among other things, a finding that the recording device was necessary to provide B.P. with a FAPE. 5

Shortly after plaintiffs requested the due process hearing, the district court entered summary judgment for the district on plaintiffs' remaining ADA, Rehabilitation Act, and First Amendment claims. It agreed with the district and found plaintiffs' claims barred for failure to have fully exhausted all remedies under the IDEA. Plaintiffs appealed that determination to this court.

While plaintiffs' appeal to this court was pending, an IDEA hearing officer from the Maine Department of Education moved forward on their hearing request. The hearing officer held a three-day hearing in March 2016 and, shortly thereafter, issued a decision. The decision rejected plaintiffs' position that the recording device was required under the IDEA. In so ruling, the hearing officer made the following findings, in relevant part:

No doubt it must be difficult to send a child who has a limited ability to communicate into the care of others. It requires a certain level of trust. The Student has attended school in the District for 12 years without a recording device, and throughout his entire educational career, he has been happy, has loved school, and has made continuous and significant progress. There have been only a handful of incidents of concern to the Parents, and the Parents have stated under oath that they felt the Student was safe at school. The need for a recording device is therefore not a safety issue. ... Everyone, including the Parents, agrees that the Student has been making good progress in his educational program. That is precisely what FAPE requires. The Student is receiving FAPE.

From a practical perspective, it is impossible for the District staff to report on every aspect of the Student's day, and it is not necessary. In the Parent's closing argument, he lists some examples where information should have been included in the daily log but wasn't, and most were essential in his eyes but not in mine or the other adjudicators who have denied his attempts to send the Student to school with a recording device.

It is unnecessary for the Student to wear a recording device to benefit educationally. As noted above, there is no *83 dispute that the student is already receiving FAPE without the recording device.

There is [a] wealth of evidence from both educators and the parent of another child with autism (Parent B) that the recording device actually would be disruptive and detrimental to the education of the Student and would interfere with the learning process. It is also understandable, given the Parents' unusually high level of scrutiny over the actions of the District, that District staff would be concerned about how the Parents would use the recordings, and that things could be taken out of context from a recording of a nonverbal child.

Based upon the evidence, I conclude that allowing the Student to wear a device that would record his day at school, either by audio or video means, would interfere with his ability to receive FAPE. The Parent was unable to state how or whether the Parents would use the recordings. There is simply no demonstrable benefit, and there is the potential for harm.

In conclusion, the Parent has failed to provide any evidence that the Student is not receiving FAPE and no evidence to support the assertion that wearing a recording device could benefit him educationally.

Issuance of the hearing officer's ruling resolving plaintiffs' IDEA claims caused this court to dismiss the original appeal of the district court's exhaustion ruling as moot and to vacate the judgment of dismissal, since, if there were an exhaustion requirement, plaintiffs had met it. See Pollack v. Reg'l Sch. Unit 75 , 660 Fed.Appx. 1 , 2-3 (1st Cir. 2016) (unpublished). 6 On remand, the district court held that the IDEA hearing officer's un-appealed findings collaterally precluded plaintiffs from establishing that the recording device was a required accommodation under the ADA and the Rehabilitation Act. The district court also found, on summary judgment, that the effective communications regulation did not apply to communications between B.P. and his parents. After plaintiffs then tried their First Amendment claims to a jury and lost, final judgment entered. Plaintiffs appealed only the dismissal of their disability discrimination claims against the district.

III.

As we described above, the IDEA hearing officer found that allowing B.P. to attend school equipped with a recording device would provide "no demonstrable benefit." So the question arises: To what extent, if any, does that factual finding preclude B.P. from establishing an essential element of his ADA claim; i.e., that the recording device would in fact provide a benefit to him in the form of greater access to the services that the district provides to its students? See Nunes , 766 F.3d at 145 .

The parties agree, and we therefore assume, that we afford the findings at issue, which were the product of an adjudicatory proceeding in a Maine administrative agency, "the same preclusive effect to which [they] would be entitled in the State's courts." Univ. of Tenn. v. Elliott , 478 U.S. 788 , 799, 106 S.Ct. 3220 , 92 L.Ed.2d 635 (1986) ; see also FPL Energy Me. Hydro LLC v. FERC , 551 F.3d 58 , 63 (1st Cir. 2008) ("A federal court is generally *84 bound under res judicata to give the same preclusive effect to a state court judgment as would be given to it by a local court within that state."); Dertz v. City of Chi. , No. 94 C 542 , 1997 WL 85169 , at *10 (N.D. Ill. Feb. 24, 1997) (holding that the doctrine of issue preclusion applies to state administrative findings for claims brought under Title II of the ADA). Maine courts apply issue preclusion, also known as collateral estoppel, "to administrative proceedings as well as to court proceedings." Portland Water Dist. v. Town of Standish , 940 A.2d 1097 , 1100 (Me. 2008). Under Maine law, issue preclusion applies when "the identical issue necessarily was determined by a prior final judgment, and the party estopped had a fair opportunity and incentive to litigate the issue in the prior proceeding." Mutual Fire Ins. Co. v. Richardson , 640 A.2d 205 , 208 (Me. 1994) (quoting State Mutual Ins. Co. v. Bragg , 589 A.2d 35 , 37 (Me. 1991) ). The application of issue preclusion "is determined on a case-by-case basis," id. , and is "meant to serve the ends of justice not to subvert them," id. (quoting Pattershall v. Jenness , 485 A.2d 980 , 983 (Me. 1984) ).

Plaintiffs also concede that the un-appealed decision of the IDEA hearing officer constitutes a final judgment and that they had a full and fair opportunity to litigate the issues necessarily decided in that proceeding. They argue, instead, that: (A) the pertinent factual findings of the hearing officer are not identical to the factual issues germane to their ADA claim, (B) the findings were, in any event, not necessary to the agency's judgment, (C) a difference in who had the burden of proof in the two proceedings makes preclusion inapplicable, and (D) events occurring after the agency judgment entered provide a basis for side-stepping the impact of that judgment in this case. Reviewing the district court's application of issue preclusion de novo, see Vargas-Colón v. Fundación Damas, Inc. , 864 F.3d 14 , 25 (1st Cir. 2017), we address each argument in turn.

A. Identical Issue

Under Maine law, issue preclusion "prevents the reopening in a second action of an issue of fact actually litigated and decided in an earlier case." Town of North Berwick v. Jones , 534 A.2d 667 , 669-70 (Me. 1987) (internal quotation marks omitted). Plaintiffs argue that, without reopening any issue of fact found by the hearing officer, they can still demonstrate that allowing B.P. to wear a recording device would be effective in providing him meaningful access to the benefits that the district offers its students. Specifically, plaintiffs argue that we should read the hearing officer's findings as trained solely on an absence of educational benefits to B.P. So limited, plaintiffs contend, the findings are not a bar to proving that the device would provide B.P. greater access to other benefits stemming from keeping his parents informed about his school day so that they can better advocate for him, more like the parents of his non-disabled peers. While we are not sure we see the distinction plaintiffs would have us draw (especially since plaintiffs themselves repeatedly portray the benefit of improved communication as facilitating their ability to obtain a better education for B.P.), the simple fact is that plaintiffs never developed this argument in the district court. The argument is therefore waived. See Teamsters, Chauffeurs, Warehousemen and Helpers Union, Local No. 59 v. Superline Transp. Co. , 953 F.2d 17 , 21 (1st Cir. 1992) ("If any principle is settled in this circuit, it is that, absent the most extraordinary circumstances, legal theories not raised squarely in the lower court cannot be broached for the first time on appeal.").

Plaintiffs did argue below that the right to a FAPE is not necessarily the *85 same as the right to an accommodation under the ADA. We agree. See Fry v. Napoleon Cmty. Sch. , --- U.S. ----, 137 S.Ct. 743 , 755-56, 197 L.Ed.2d 46 (2017) (noting that the ADA and the IDEA have "diverse means and ends," even though "the same conduct might violate" both statutes). This argument, though, overlooks the fact that issue preclusion applies not only to determinations of law, such as whether the IDEA or the ADA has been violated, but also to determinations of fact made in resolving issues of law. See Godsoe v. Godsoe , 995 A.2d 232 , 237 (Me. 2010) ("A party may be collaterally estopped from relitigating a factual issue even if the two proceedings offer substantially different remedies or the second proceeding is based on a different claim than the first."); see also Restatement (Second) of Judgments § 27 cmt. c (1982) ("An issue on which relitigation is foreclosed may be one of evidentiary fact, of 'ultimate fact' (i.e., the application of law to fact), or of law."). In short, when we consider issue preclusion rather than claim preclusion, it is very often the case that the ultimate question in the earlier proceeding will differ from the ultimate question in the later proceeding. See, e.g. , Napier v. Town of Windham , 187 F.3d 177 , 184-85 (1st Cir. 1999) (applying Maine issue preclusion principles and giving preclusive effect to findings from a state criminal case in a subsequent federal civil rights suit); Gray v. TD Bank, N.A. , 45 A.3d 735 , 737-38, 742 (Me. 2012) (giving preclusive effect to findings from a probate proceeding brought to determine whether certain funds held by a bank were the property of the estate in a subsequent breach of contract case brought against the bank). That difference does not mean that a predicate factual question in each case cannot be identical. See Gray , 45 A.3d at 742 ("[T]he factual question at the center of Gray's breach of contract claim against the Bank is identical to the question adjudicated and determined in the Probate Court ...." (emphasis added) ). And here, plaintiffs neither dispute that the question whether the recording device would benefit B.P. is at "the center of" their ADA claim, nor offer any properly preserved argument that the claimed ADA benefit is any different from the educational benefit that the hearing officer found was lacking under the IDEA.

B. Necessary to the Judgment

Plaintiffs' principal argument is that the hearing officer's finding of no demonstrable benefit, even if identical to an issue upon which they need to prevail in order to successfully make out a reasonable accommodation claim, was not necessary to the hearing officer's final decision. They advance two versions of this argument: first, that the hearing officer's finding of "no demonstrable benefit" was an unnecessary alternative ground for her decision, and second, even if considering the effectiveness of the device was necessary, there was no need for the hearing officer to find that the device offered no benefit whatsoever. We address each argument in turn.

1.

The hearing officer wrote that "[e]veryone, including the Parents, agrees that the Student has been making good progress in his educational program." She went on to state: "That is precisely what FAPE requires. The Student is receiving FAPE." As plaintiffs see it, the hearing officer could have stopped there. Indeed, by plaintiffs' most recently advanced logic, even if the hearing officer had concluded that the recording device would be quite effective and beneficial, she would have been required to rule against the parents if B.P. was nevertheless already receiving a FAPE. And, plaintiffs say, the hearing officer's *86 finding of no demonstrable benefit could not be appealed because the judgment could stand independently on the finding that B.P. was receiving a FAPE. See Restatement, supra , § 28 cmt. a ("[T]he availability of review for the correction of errors has become critical to the application of preclusion doctrine.").

Read as a whole, though, the hearing officer's decision does not invite us to construe the "no demonstrable benefit" finding as only an alternative ground for the decision. The ruling never labels the finding as an unnecessary or alternative part of its reasoning. To the contrary, the hearing officer's statement that B.P. is "receiving FAPE" follows-and seems to be based on-a discussion of events belying any need for the recording device. Additionally, the decision twice labels its finding regarding the efficacy of the device as its conclusion. 7 In this manner, the text invites the reader to see the finding of "no demonstrable benefit" as reinforcement for the legal conclusion that B.P. was receiving a FAPE, rather than as an unnecessary alternative basis for the decision's ultimate conclusion that the device was not required under the IDEA.

The nature of the hearing that gave rise to the finding supports reading the hearing officer's conclusion as standing on two reinforcing-rather than alternative-grounds. Regarding the recording device claim, the proceeding was structured to determine, in the words of the district court's initial summary judgment ruling requiring exhaustion under the IDEA, "whether B.P.'s IEP should include his use of supplementary aids to properly protect B.P. at school or allow B.P. to effectively communicate and advocate for himself so that he could best work towards his educational goals." Not surprisingly, therefore, much of the hearing focused on whether and to what extent the recording device would benefit B.P. by allowing him to best pursue his educational goals. All parties, especially plaintiffs, treated this as a central question in the IDEA proceeding and they therefore made their best case on this issue. In particular, plaintiffs emphasized that B.P. required the device for safety reasons, to "protect himself," as well as to advocate for himself through his parents. At the hearing, B.P.'s father testified that without the device, "there is no way for [B.P.] to tell us what happens ... and, therefore, for him to ... advocate for himself or get our assistance in advocating for him." B.P.'s mother testified similarly. Plaintiffs maintained this position in the written closings they submitted to the hearing officer. Plaintiffs also claimed that the device was necessary to allow them to reinforce at home the programming provided at school. In response, the district elicited testimony from its staff that the device would not support B.P.'s education and could in fact hinder it by increasing his isolation and making staff and his peers uncomfortable. Given this extensive and predominant focus on the potential benefits of the recording device, we decline plaintiffs' invitation to presume that the hearing officer's finding that B.P. was receiving a FAPE would have remained unchanged had the parents convinced the officer that B.P. would indeed benefit from wearing the device. We find additional support for our conclusion in the fact that the hearing officer, in her ruling, expressed puzzlement that the parents failed to explain *87 precisely how they would use the recordings. 8

Substantive IDEA law buttresses our reading that the hearing officer's "no demonstrable benefit" finding was not an unnecessary addendum, but rather served as an important reinforcement of the decision that B.P. was already receiving a FAPE. It is true that a school need not maximize the benefits received by a student in order to provide a FAPE. See Endrew F. ex rel. Joseph F. v. Douglas Cty. Sch. Dist. RE-1 , --- U.S. ----, 137 S.Ct. 988 , 1001, 197 L.Ed.2d 335 (2017) (rejecting an argument that a FAPE must provide students with disabilities "substantially equal" opportunities to those afforded students without disabilities). At the same time, though, the IDEA establishes no objective tool to measure how much of an available benefit the school must provide. See id. at 1000 n.2 ("We declined to hold in Rowley , and do not hold today, that 'every handicapped child who is advancing from grade to grade ... is automatically receiving a [FAPE].' " (alterations in original) (quoting Bd. of Ed. of Hendrick Hudson Cent. Sch. Dist., Westchester Cty. v. Rowley , 458 U.S. 176 , 203 n.5, 102 S.Ct. 3034 , 73 L.Ed.2d 690 (1982) ) ). Rather, the IDEA requires a hearing officer to pay heed to the precise circumstances confronting an individual student. See id. at 999 ("To meet its substantive obligation under the IDEA, a school must offer an IEP reasonably calculated to enable a child to make progress appropriate in light of the child's circumstances ." (emphasis added) ). The statute directly calls for consideration of the "unique needs" of each child, 20 U.S.C. § 1400 (d)(1)(A), and of the possibility that "supplementary aids" may need to be included in a child's IEP, id. § 1414(d)(1)(A)(i)(IV). A careful hearing examiner confronted with the parents' claim that a recording device would meaningfully benefit B.P. in a manner relevant to his receipt of a FAPE might well have thought it important-as plaintiffs themselves apparently did-to assess all the potential benefits of the device before finally reaching a conclusion that B.P. was receiving a FAPE.

The distinction between a substantive deprivation of a FAPE and a procedural deprivation of a FAPE may also have accounted for the hearing officer's assessment of the extent to which the device would benefit B.P. A substantive inquiry focuses on the "proper content of an IEP." See Lessard v. Wilton-Lyndeborough Coop. Sch. Dist. , 518 F.3d 18 , 23 (1st Cir. 2008). A procedural inquiry instead focuses on the parents' ability to participate meaningfully in the IDEA process. See id. (citing the right of parents to be part of the IEP team as an example of the IDEA's procedural requirements). Our review of the IDEA due process record suggests that there was a fair amount of confusion, or at the very least an evolution throughout the proceedings, regarding whether the hearing officer was adjudicating a substantive challenge or a procedural one, or both. Compare 20 U.S.C. § 1415 (f)(3)(E)(i) (substantive) with id. § 1415(f)(3)(E)(ii) (procedural). Although the hearing officer initially believed that she was adjudicating a substantive challenge, she ultimately framed the issue in her opinion in the words of a procedural challenge. And between plaintiffs' first closing argument and their reply closing, they seem to have subtly changed from emphasizing the substantive nature of their claim (that B.P. was substantively deprived of a FAPE because *88 he lacked the ability to protect himself and advocate for himself) to emphasizing its procedural nature (that without the device, the parents were deprived of their procedural right to participate in the IDEA decision-making process, which in turn deprived B.P. of the ability to protect himself and advocate for himself). In light of this apparent evolution, the hearing officer's analysis (and her multiple conclusions) can reasonably be read as inquiring into both whether B.P. was substantively deprived of a FAPE and whether he was procedurally so deprived. So viewed, the "no demonstrable benefit" finding may have been necessary to rejecting the IDEA claim even if it was not necessary to finding that B.P. was not substantively deprived of a FAPE.

For these reasons, and for purposes of considering the preclusive effects of the hearing officer's findings, we are not persuaded that an assessment of the efficacy of the recording device was unnecessary to the FAPE proceeding. See Manganella v. Evanston Ins. Co. , 700 F.3d 585 , 593-94 (1st Cir. 2012) (rejecting plaintiff's argument against issue preclusion because "although [plaintiff] argues here that the arbitrators could have just assumed the truth of the harassment allegations [and reached the same result], he did not ask them to do so" but rather "vigorously litigated" their truth); Restatement, supra , § 27 cmt. j ("The appropriate question, then, is whether the issue was actually recognized by the parties as important and by the trier as necessary to the first judgment."). Moreover, a rationale we have cited for the requirement that a finding be necessary to the judgment-that the parties do not have a strong incentive to litigate a peripheral issue, see Commercial Assocs. v. Tilcon Gammino, Inc. , 998 F.2d 1092 , 1097 (1st Cir. 1993) -shrinks considerably where the parties have vigorously litigated the issue before a tribunal that to all indications viewed the issue as important. Here, the parties and the hearing officer had ample cause to regard a full assessment of the potential benefits of the recording device as relevant to the determination of whether B.P. was receiving a FAPE (and thus as necessary to the overall agency judgment), and appear to have acted accordingly.

Plaintiffs' argument that they had no incentive to appeal the hearing officer's ruling therefore lacks the full force it might have had were it clear that the finding that B.P. was receiving a FAPE stood entirely on its own without any reliance on the "no demonstrable benefit" finding. If a reviewing court agreed with our reading of the hearing officer's decision, then it would have entertained an appeal of the latter finding. And if it disagreed with our reading, plaintiffs' argument on preclusion would have been substantially strengthened. In sum, plaintiffs likely had ample incentive to appeal the hearing officer's judgment if they felt that the "no demonstrable benefit" finding was plainly wrong.

2.

This brings us to plaintiffs' closely-related fallback theory: that, even assuming some assessment of the efficacy of the recording device was necessary to the judgment, the hearing officer did not need to decide that the device actually lacked any benefit at all. Rather, all the officer needed to find on this score, say plaintiffs, was that the device was not so effective and important as to be necessary for a FAPE; her additional finding that the device would provide no benefit at all, much less that it would interfere with the provision of a FAPE and could affirmatively cause harm, was simply "not the standard"

*89 and was therefore unnecessary to the judgment.

In rejecting this argument, we do not reject plaintiffs' contention that, in theory, the hearing officer could have concluded that the recording device would provide some benefit, yet not enough that its provision was necessary to provide B.P. with a FAPE, and still have reached the same result. Cf. K.M. ex rel. Bright , 725 F.3d at 1101 ("[T]he IDEA does not require schools to provide equal educational opportunities to all students." (internal quotation marks omitted) ); Endrew F. , 137 S.Ct. at 1001. But we resist the temptation to "speculate that a prior decision could have been rested on narrower grounds than those actually chosen." Wright & Miller, supra , § 4421. As we have previously observed, "a factual determination is not inherently untrustworthy just because the result could have been achieved by a different, shorter and more efficient route." Commercial Assocs. , 998 F.2d at 1097 .

Plaintiffs cite no authority for their argument to the contrary. The Restatement is silent on the matter, despite a thorough discussion of the preclusive effects of "evidentiary facts," i.e., those that are not ultimate facts. Restatement, supra , § 27 cmt. j; id. § 27 ill. 17. Our survey of Maine case law has revealed no hint that Maine courts would embrace a rule that issue preclusion applies only where a finding on an issue necessary to the judgment is the narrowest possible finding on that question. In fact, several Maine cases suggest the opposite. See Perry v. H.O. Perry & Son Co. , 711 A.2d 1303 , 1305 (Me. 1998) (giving preclusive effect to a finding that "[t]he record is devoid of any evidence" of detrimental reliance); Button v. Peoples Heritage Sav. Bank , 666 A.2d 120 , 121, 123 (Me. 1995) (giving preclusive effect to a finding that "all of [decedent's] actions in arranging her financial affairs were voluntary," where the only relevant action was the redemption of a particular certificate of deposit (internal quotation marks omitted) ). So, too, does precedent applying the preclusion principles of other states. See Gambino v. Koonce , 757 F.3d 604 , 609-10 (7th Cir. 2014) (rejecting appellant's argument that the first court's finding of fraudulent intent was not necessary to the judgment because its decision on liability could have rested on a finding of recklessness and its award of punitive damages on a finding of gross negligence); cf. Stoehr v. Mohamed , 244 F.3d 206 , 209 (1st Cir. 2001) (per curiam) (rejecting an argument against issue preclusion on the grounds that the first court's finding of fraud was not essential because liability under Mass. Gen. Laws 93A need only be premised on unfair conduct). But cf. NLRB v. Thalbo Corp. , 171 F.3d 102 , 111 (2d Cir. 1999) (noting that, where the magistrate judge believed that a Title VII claimant was required to seek other work "aggressively," a finding that the claimant did not search for other jobs at all would have been "superfluous").

In assessing the implications of the foregoing discussion of the necessity requirement in this case, we are guided by Maine's recognition that "collateral estoppel is, after all, a flexible doctrine," Pattershall , 485 A.2d at 983 (quoting Hossler v. Barry , 403 A.2d 762 , 769 (Me. 1979) ), and its understanding that the doctrine "is 'meant to serve the ends of justice not to subvert them,' " Mutual Fire , 640 A.2d at 208 (quoting Pattershall , 485 A.2d at 983 ). We have previously taken a pragmatic approach in applying issue preclusion principles. See Miller v. Nichols , 586 F.3d 53 , 62 (1st Cir. 2009) (applying Maine law and rejecting an argument against issue preclusion in part because it "ignores ... what actually happened in the state court proceedings");

*90 Commercial Assocs. , 998 F.2d at 1096 (noting that Rhode Island courts "allow themselves a good deal of latitude in applying the rule [of collateral estoppel], observing the spirit of it rather than the letter" (alteration in original) (quoting Hill v. Bain , 15 R.I. 75 , 23 A. 44 , 44 (1885) ) ). We do the same here, and decline to adopt the unbending application of the necessity requirement urged by plaintiffs. The parties to the prior proceeding litigated a factual issue as if it were the essential issue in the case, the applicable law provided no clear sign that resolution of the issue was a frolic, and there is nothing about the substance of the resulting finding to cause one to think that it was not the product of a seriously undertaken decision by the adjudicator. In this context, we conclude that the purposes underlying the necessity requirement are adequately satisfied.

C. Burden of Proof

We turn now to plaintiffs' third argument: that, under Maine law, when the party against whom preclusion is sought bears the burden of proof in the first proceeding but not in the second, findings of fact in the first proceeding are often not given preclusive effect in the second proceeding. See Crawford v. Allied Container Corp. , 561 A.2d 1027 , 1028 (Me. 1989) ; see also Restatement, supra , § 28(4). But that is not the case here. Rather, as ADA claimants, plaintiffs must carry in this second proceeding the burden of proving that the proposed accommodation-the recording device-will be beneficial, i.e., will provide some increased access to a public service. See Reed , 244 F.3d at 258-59 . Similarly, they bore the burden in the IDEA proceeding of showing that the device was necessary for B.P. to receive a FAPE. In short, on de novo review we find that there was no relevant shifting of the burden.

D. New Evidence of Pretext

Plaintiffs argue, finally, that evidence that has come to light since the IDEA hearing suggests that the district's refusal to allow the recording device was pretextual. This evidence, plaintiffs contend, creates an issue of material fact "concerning the validity of the very finding the district court deemed preclusive." Plaintiffs point specifically to evidence that the district's special education director agreed to allow them to view video recordings of B.P.'s speech-language therapy only if they promised not to use the recordings as a basis for a complaint against the therapist. They also rely on evidence that the director prohibited them from visiting B.P.'s school unannounced because they were solely focused on seeking out wrongs by school staff.

Even if, as plaintiffs suggest, the new evidence establishes an issue of material fact as to whether the district's refusal to allow the device was pretextual, it has no impact on this case. Pretext is only relevant to the final stage of the ADA analysis. Once the plaintiff has shown that the accommodation sought is reasonable and effective and the defendant has claimed undue hardship, then the plaintiff has the opportunity to prove that the defendant's claimed hardship is pretextual. See Wynne v. Tufts Univ. Sch. of Med. , 976 F.2d 791 , 796 (1st Cir. 1992) (explaining that, when pretext is at issue, plaintiff must produce specific facts that undercut the defendant's position). Here, the analysis does not even get past the very first step. Because of the hearing officer's factual findings, plaintiffs cannot make the preliminary showing that the device would benefit B.P. in some manner. And because plaintiffs do not dispute that proving that the device would benefit B.P. is essential to sustaining their reasonable accommodation *91 claim, they cannot prevail. 9 No amount of pretext evidence can change that result.

IV.

For the foregoing reasons, we affirm .