Oh c’mon, athletic departments of schools that build or own stadiums are separate entities from the school, and are often a cash cow for a school. They can and do issue bonds to build or renovate, they will rent (from their own school) the facilities a school owns, they sell naming rights for tens of millions even for temporary naming, they reap untold millions in licensing.
Doubtless some may siphon off a small bit off the tuition revenue stream, but students don’t pay for those shiny stadiums… unless they pay taxes, because with all those revenue streams into athletic depts that turn a profit, guess who foots the largest portion of stadium building costs, be they for a city or college team? You guessed it, the same people having their wages forcibly taken, and everyone else too.