They don't NEED proof. Private employers don't have to have a trial, a hearing, or a grievance process before making employment decisions, unless there is some binding agreement that holds them to such a process - otherwise you're employed "at will" - meaning you're free to leave, or they're free to terminate you. They can fire you for ANY reason that isn't protected by law. The boss could have fired you for wearing a color of shirt he didn't like. They can even fire you based on gossip about what was on your Facebook page, whether it was actually there or not, or if they ever saw it or not. If they were annoyed hearing about it, and your name was connected to it, that's a reason (note that REASON is not the same as "for cause", which plays a part in determining unemployment benefits and has it's own process. Make sure you file for unemployment ASAP.). The only people they have to convince that it was a good ENOUGH reason is whoever above them in the chain of command might ask.

