I don’t think the student needs to own property in Austin. Back in the day, a student could own real estate anywhere in Texas to get this discount…and there are some areas in Texas with very inexpensive pieces of land that would have sufficed back then.
However, this doesn’t change that this student would be admitted as an OOS applicant, with a much lower chance of admission than instate students have (and UT A isn’t exactly a cakewalk for admissions for instate students).