The University can't really "privatize" the greek system without shooting itself in the foot. There are so many prestigous UA greek alumni who support the University (for example: the Governor and U.S. Congressmen & Senator, as well as wealthy businessmen & women). The University can't afford to make those people mad.
Plus, the University doesn't own the fraternity/sorority houses. The organizations own their own houses. The University owns the land that the houses are built on, and they lease the land to the organizations at a low rate. The only thing they could do is raise the lease rate to something completely unreasonable OR refuse to lease the land at all. Because the greek system at UA is so powerful, I sincerely doubt that the University administration wants to risk losing all control over the greeks, along with donations from greek alumni.
On another note, I've been told that the Administrator is *very* angry at the faculty senate and this professor in particular for bringing so much bad publicity to the University.
Just my two cents...