Neither MIT nor Harvard are public schools, they are both private.
However, I do think that there should be more mechanism than the purse to persuade institutions to make material accessible to disabled populations -- but for major institutions only, since I'm not sure smaller organizations can cope with the burden. Perhaps organizations above some revenue?
If central government just gave them a stipend and didn't specify the projects it was to be used on then the argument you're supporting would perhaps have some mileage; but it's payment for a specific service. If the schools aren't making their research centres accessible or are unnecessarily excluding disabled people [from research related tasks/benefits/etc.] then, yes, this argument would be valid.