Show me the incentives....
Obvious counter-move for the elite universities: Detail every student's disabilities & accommodations on their transcripts, to assist potential employers and graduate schools in anticipating their special needs.
If I had someone spontaneously tell me a potential hire were disabled I would block all communication from that someone. Way too much risk.
Does anyone legitimately think that those are not used as factors for candidate selection?
Probably yes. The college's motive is to axe the rate of mendacious malingering; pushing beyond that could give them legal costs without commensurate benefits.