AEPhi will allow chapters to operate unrecognized by the university. Example: We had a colony at Brandeis a few years back. As an area alum, I was invited to the colony's new member ceremonies. I remember being told distinctly not to wear anything that might make it look like I was going to a ritual, because GLOs were not recognized by the school. That colony had to operate wayyy underground.
Harvard doesn't recognize fraternities and sororities either. There are chapters of Kappa Alpha Theta, Delta Gamma, and Kappa Kappa Gamma is colonizing - so that means either those 3 sororities are on the "will colonize if unrecognized" list, or they made an exception because it's Harvard.