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].