Ok. So I looked at the FY19 budget for one of the universities I attended and for the overall budget of $7.3 billion it's broken out like this (numbers are rounded). [1]
Tuition and fees -> $1.8 bb
Government appropriations (it looks like this is what you're referring to as direct subsidies?) -> $ 470 mm
Grants and contracts -> $862 mm
Sales & Services University -> $543 mm
Sales & Services Health System -> $3.3 bb
Sales & Services OSU Physicians -> $480 mm
Gifts and Endowment -> $380 mm
Negligible other items -> $100 mm or something.
So what subsidies are you referring to? Happy to look at a different university if you want to provide an example.
[1]https://busfin.osu.edu/sites/default/files/12_a_fy21_budget_...
-edit-
Unfortunately I can't reply, but I'm not sure why you're only considering government appropriations with respect to tuition instead of the entire budget. Seems a bit selective to me.