Some of that is probably because students at elite universities come from families who understand exactly how to navigate meritocratic systems. Parents who know you need a tutor to ace the ACT and an essay editor to polish your application essays likely also understand that, in some situations, you should get a psychiatric evaluation and disclose any diagnoses so you can receive accommodations.
I'm fairly convinced a big part of clearing the barrier to entry of these elite institutions is having a deep understanding of exactly the things you need to do to succeed given the structure of the system and the nature of the competition. Students at "non-elite" institutions are more likely to come from backgrounds where even if you DO have a disability, maybe nobody ever tells you that you can go to the doctor for it, or that something like "accommodations" exist to help you.
I'm fairly convinced a big part of clearing the barrier to entry of these elite institutions is having a deep understanding of exactly the things you need to do to succeed given the structure of the system and the nature of the competition. Students at "non-elite" institutions are more likely to come from backgrounds where even if you DO have a disability, maybe nobody ever tells you that you can go to the doctor for it, or that something like "accommodations" exist to help you.