UT athletic teams are fully funded, so they give what they can as allowed by the NCAA. And yes that means some students get nothing at all.
Agree that just because a website says there are full scholarships doesn’t mean everyone applying has even a slight chance at one. Please consider the California schools. It’s a big state and you can be independent somewhere 5 or 6 hours from your home. It’s hard to get parents to talk finances, but maybe you can get them to do a sample FAFSA and get an idea of where you stand.
You can also show them how much a comm college will cost.