Hmmm, I suspect that the "free" tuition is on top of things like Pell Grants (federal assistance). The kid fills out the FAFSA and gets some federal assistance, then UT tops that off to cover tuition.
UT Austin's tuition and fees are about $14,000 per year. A federal Pell Grant might be around $5,000 per year. So they are shaving maybe another $9,000 per year off of annual expenses.
The kid still has to pay for housing and food, but the kid would have had to pay for housing and food *somewhere* for four years. UT Austin estimates those "other" costs at around $20,000 per year, and around $13,000 per year if the kid is living with their parents.
Students costs through work-study programs (like working for Rec Sports or at the library) and some have part-time jobs off campus. Some are doubled up on housing (two to a room) and are paying half the "normal" rent. Some have efficiency rentals that are reserved for low income students. Many get summer internships or stipends during their last few years on campus as they get farther along in their degree.
The "free tuition" takes off a layer of cost to make it a little easier. Not completely paid for, but one step towards a more level playing field.