If there is nothing in your student handbook that says you can't have local GLO's, that is all the documentation you need. Some schools do have this rule - here's an example:
http://www.lhup.edu/stulife/student_...ions.htm#greek
Basically you don't have to prove why you should be there, she has to prove why you shouldn't be. I forgot to ask - is she saying she wants you to affiliate with a national or she wants you gone, period?