Do they honestly think they'll be able to make a statement like that without a current student or alumnus coming out and refuting it to the media? If so, they are an extremely deluded bunch.
They are entitled to say whatever they want, but if they try to say that they represent the whole campus officially, they will just end up looking like jerks.
The school really can't do anything, any more than they can do anything about the party school rankings (there's a jump for you). Now if one of the members of the org stole official stationary from the admin and released a statement on it - or if the org said that "President Whosit backs us" and he doesn't - then that's another story, and they could get in mucho trouble.