Doesn't that parenthetical comment destroy the rest of the [small sub-]argument: because you paid someone for doing research doesn't mean that if they decide to make something else free to access that you have a right to make further demands of them.

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.