I don't know about the legal issues, but from a common-sense perspective it would make more sense for the captioning to be performed on-demand on a per-video basis; i.e. if a disabled student needs access to a particular video, he/she can request that it be captioned. The captioning is then added to that video and made available to everyone.
That way the ADA students get the captioning they need, and everyone else gets the benefit of the videos as well; plus the captioners don't spend a lot of their limited time captioning video that nobody will actually use the captions of; rather they spend their time captioning videos that actually need captioning sooner rather than later.
You know that will not work because when word gets out that this is the modus operandus, bogus requests will get made for each and every video in order to have every video captioned.
What I don't understand is that people can in such way take a situation hostage so that the end result is that no one has access.
"What, #random disability has no access? Than NO ONE has acces!"
That's like saying buses can't run because #random disability can not use them.