You're right, TV money does. Here is an
item on Les Miles' salary while he was at LSU. He got $300,000 from the state of Louisiana. The rest of his salary came from the athletic department's SEC TV money. Here is an
item on Saban. It says his salary is $245, 000, I'm willing to bet the only part of his price tag paid by the taxpayers of Alabama, and a "talent fee" of $6.48 MM, that's paid by the athletic department. IIRC, Bronco Mendenhall (and Daisy Fuente at VPI) is paid $100,000 from state money and the rest of the salary is from the athletic department funds. The coaches are paid a lot. They are not necessarily the highest paid state employees as much as they are the highest
compensated state employees when all the non-state sources are added in to their state salary.