Tilman definitely gets a very very big say in sports at UH, especially since he is the one dishing out all the money for coaches and what not, but Khator could still block briles. They are both loved there and have done great things with their athletics, but Khator could still shut him down when it comes to hiring Briles or any coach under a sexual scandal. She has improved that school immensely and is treated like a god there.
At the UH vs OU game this year, they welcomed the Mayor of Houston and there was a light applause but without even introducing her, the camera panned to her and the crowd went nuts. Pretty sure RGT doesn't get that same reception.