Indeed, I thought about bringing this up earlier. Two of Mexico's top soccer teams, Pumas and Tigres, are owned by UNAM (maybe the largest university on the planet, depending on who's counting) and the Autonomous University of Nuevo León. A third team, Leones Negros, is owned by the U. of Guadalajara, but they are not currently in the top division.
In all three cases, the teams play in stadia owned by the university, and are operated as a business. There's no requirement whatsoever that players be students.