Well I suppose that's true if it cost 0 to actually attend a University. But buildings and professors and everything else cost a lot of money so why shouldn't the athletic department pay that expense?
If your athletic department "operates in the red", then who covers the cost to make it break even? The university. If the university is having to cover the financial difference, then what material difference does it make?
It's just accounting semantics with fungible money. They
could allow the the athletic department to show a profit on the income statement, and then sweep the net profit over to the university to pay other university expenses that you mentioned. But it's disingenuous to pretend that so many athletic departments operate in the red when they are forced to run in the red by their own university's accounting practices.