What stops a university from doing whatever they want when an academic misconduct allegation arises?
What's to stop him?  His ethical considerations, and the paper trail that was created.

If you prove you had permission, what's to stop the university from doing whatever they want?

Your university will have policies in place, and procedures for filing internal complaints.  Your energetic self-defense, using your paper trail and university policies and procedures, would be what would stop the university from doing whatever they want.

You might also be able to file a complaint with your state education department.

I don't know anything about lawsuits, except that they can take a long time.  Perhaps it would help to post at Law SE.