You missed my earlier post which explained that commercial patent royalties are considered unrestricted funds and are used to pay for stuff that the government finds unallowable to pay with taxpayer money.
That's the fundamental difference with private schools who sit on big endowments (also unrestricted funds).
In general, with any company or organization accepting taxpayer dollars, money must be obtained and spent for the purposes it is designated for. That is, tuition expenses are paid with tuition dollars, research expenses are paid with research dollars. If the university cannot pay for all tuition expenses, they can't reach into the research pot, they have to up the tuition.
To give an example of how extreme this separation is, where I went to school there were several locations by cafes where they put two differently styled outdoor trash cans next to each other. One trash can was emptied by people from campus foodservice, which is considered an unrestricted, auxiliary organization, and the other trash can was a general campus trash, which can be paid out of restricted taxpayer funds. Technically, it was illegal to throw cafe trash in the campus trash can.