Freedom of assembly is right there in the first amendment to the US constitution.
USC is a private institution.
College isn’t the government, it is an organization you choose to voluntarily enter into a relationship with, as such it is free to have rules about your conduct, including rules forbidding you from joining other organizations. They also have rules for the frats and sororities as that too is a voluntary relationship and they are under no compulsion to certify them as parts of the university.
Exactly right. Just because they are paying to sit in a classroom a few hours a week, it does not follow that one would give up ones freedom of association.