Auxiliary revenues and student fees cover most of the other budget that is referred to as "subsidy", which are things like bookstore revenue etc. Looking at the budget, the state literally provides zero dollars directly to the athletic department from a technical accounting perspective.
Granted one could argue that is just accounting and they are diverting the money from other things to go to the athletic department and that University money in general is state money, but on an accounting basis, no tax dollars technically go to the AD budget at all, it is all University Revenue one way or the other.
And as I said before, you were claiming this is some secret stuff, it is not and you seem like a smart dude so google it, it's all on the internet.