“authorized entity” means a nonprofit organization or a governmental agency that has a primary mission to provide specialized services relating to training, education, or adaptive reading or information access needs of blind or other persons with disabilities;
Sounds like the exact same website could be setup and remain the right side of the legal boundary simply by presenting themselves as a service for the deaf. YMMV.
The owners would have plausible deniability I feel, they don't know whether their users are deaf. Then it would be down to the copyright owners to address whether individual users had rights to format-shift audio tracks [they purchased] in to a format they could consume [specific language subtitles].
(Granted, that the "phonorecord" must be in a "specialized format exclusively for use by blind" is fuzzy.)