CYA academic scheme. In our humble opinion it really seems like overkill to require such an opinion for this scenario and under these conditions ... but hey, it's been a long time since we went to school and we assume that litigation crazed copyright owners have altered the academic climate. Maybe we can find a way to save Betty White!
Fair use opinions. Yes, fair use statements are often drafted by lawyers for movie companies who need them for the benefit of insurance companies. In fact, insurance companies often pre-select attorneys for these legal opinions based on their expertise and experience. Such statements provide an opinion supported by current case law.
Permission from Betty White? Betty White has the right to halt commercial uses of her image under right of publicity rules -- for example, in ads or to imply endorsement of a website. But, unless she owns the copyright to the photo, no permission from Betty White is required to use her poster for a documentary film.
Statement of Best Practices. We think your situation is an ideal one to apply the Documentary Filmmakers' Statement of Best Practices in Fair Use (prepared by The Center for Social Media). the Statement "makes clear what documentary filmmakers currently regard as reasonable application of the copyright fair use doctrine ..." and has been accepted by numerous broadcasters as well as four insurance companies, thus simplifying the clearance practice and avoiding expensive opinion letters. You should review that document and attempt to fit your use into one of the four classes. For example -- if the subject of the film (not the documentary maker) acquired and used the poster, your daughter may make a convincing argument using the third class of situations -- "Capturing Copyrighted Content in the Process of Filming Something Else." You may also benefit by reading up on the "transformative" aspect of fair use as well as looking at some summaries of fair use cases.
If fair use does not apply ... If fair use does not excuse the use, you would need permission from the person who owns the rights to the image on the poster, typically the photographer.