Earlier quoted context omitted.
These organizations literally directly receive money from the government. Students grants are a factor too, but they are owned and financed in large part by the State. That's called a subsidy. They are losing money, that the taxpayer shoulders.
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 S…
So if you want to look at total cost starting from the average amount a student pays as tuition you have to increase it by 38%. There are of course other intangibles paid for by the government such as the initial investment, often the land and a part of the endowment too.
So it is consequence fair to say that that tuition in state university is subsidized by the government.