". . .do they make their own students pay to attend home games?"
I don't know about OU, but I have students at another Big 12 school. Purchasing football tickets -- or tickets to any extracurricular activity -- is not added into required tuition and fees. Rather, it is an option.
Even with a sports pass, the students have to go "pull" tickets the Monday morning before the game to get their assigned seats. It's not first-come, first-served in those huge stadiums.
Priority is given according to class rank. If they want to sit with friends, one member of the group collects the others' passes and pulls tickets together for all of them. I'm sure students can buy any available tickets if the game is not sold out.
Ah, what I am missing by going to a small, Christian college.