The short answer is yes.
If you are ever pulled over by the University of Texas RGV (or whatever) anywhere in the state, don't argue jurisdiction. They can not only stop you in Brownsville even though you're miles removed from the campus next to Texas Southmost College downtown, they actually have more jurisdiction than the Brownsville Police Department or the Cameron County Sheriff's Dept.
In fact, they have even more jurisdiction than do constables, whose jurisdiction extends over to a neighboring county from the one where they were elected.They have primary jurisdiction on at least 85 Texas counties where there is a UT System facility and another 30 or adjoining counties where they have secondary jurisdiction. This includes all of Cameron, Willacy, Hidalgo and Starr counties, among others. (See graphic)
They just added Comal County in July this year.
The University of Texas Policy and Procedure Manual states that "the primary function of peace officers commissioned by the University of Texas System Police includes all counties in which property is owned, leased, rented, or otherwise under the control of the University of Texas System."
Given the reach and breadth of the UT Megasystem, this would include virtually every corner of the state. And their role is not merely to protect UT System property, their jurisdiction very nearly approaches that of their sister law enforcement entity the Texas Department of Public Safety.
UT System Police are vested with all the powers, privileges and immunities of peace officers, may arrest without a warrant any person who commits a crime, and may enforce all traffic laws on streets and highways within those counties.
But that is not all.
These guys can also can render assistance to other agencies if they are summoned in accordance with Chapter 14, Code of Criminal Procedure. That means that they can be there with the Border Patrol or Customs if they are called to help.
So if you see the U Cops black-and-whites turn on his lights in your rear view mirror, don't even think of making the lack-of-jurisdiction argument. You'd almost have to go all the way to the checkpoint in Sarita before they run out of their turf.
https://www.utsystem.edu/pol/policies/105JurisdictionFINAL.pdf