The university also has a duty to maintain a hostile-free environment. Your free speech is my hostile environment.
Here is the code of student conduct for OSU.
http://studentlife.osu.edu/csc/
My understanding from my adviser days was that GLOs formally recognized by the university are considered as "guests" on campus. Meaning, any action done by the GLO that is not in alignment with the school can be penalized, including being no longer recognized by the school. Thus, "kicked off campus".
Maybe these GLOs should fight the school and sue. Maybe they would win. But, that is just going to make it harder for the remaining GLOs to operate on campus.
If it comes down to the university being sued by every GLO, then it would be in the university's interest to no longer allow GLOs on campus.
You (the general you) really need to see the big picture. One incident of one chapter can have repercussions on all GLO chapters.
That is why I think PiKA nationals came out with their statement about themed parties.
A chapter who sues and wins the lawsuit wins the battle, but could loose the war by making it hard for other GLOs in the future.
And, maybe I am looking at this from a NPHC point of view. We generally have a very tight hand on our undergraduate chapters and members. It is nothing for us to expel individual members and pull chapter charters for conduct deemed unbecoming of the org.
You can find expelled members and chapters on our public website.
http://www.sgrho1922.org/expulsions-suspensions