It looks like each University branch sets it’s own rules for how their IDs are issued. According to the University of Texas — Austin web page, their CIO sets the rules and they do verify the holder’s ID:
“No person will be issued an ID Card until the identity of the individual can be verified and the authenticity of foundation identification documents can be established. Identification documents presented must be issued by an appropriate governmental agency and contain a photographic or digital image.”
Sooo… where does that leave us? To get a UT-Austin student ID you need some other form of ID issued by a governmental agency that has your picture on it like… a driver’s license or a passport.
UT-Dallas uses what they call a “Comet Card” as a student ID (it serves several other functions as well…) and to get one, again, you need to prove your identity through a driver’s license or a passport.
So if you have a driver’s license or a passport to get a student ID, why not just use that when you go to vote since either is an acceptable voter ID?