Really?

Some professors have “hard money” jobs where the university covers most/all of their salary; startup packages that are meant to help you get a grant are pretty common, as are fellowships or TAships for students.

However, I don’t think most universities cover much of the actual research expenses.

As for the patent, most places offer a split with the inventor, and may not patent everything; they have a right of first refusal though.

If the university is publicly funded, then it is the public who actually paid for the research.