What has not been completely established is the exact nature between Petrino and this girl. Is it sexual and how long has it been going on? NOTHING has been decided yet. He may very well survive this, depending on the facts that have yet to come out.
@poooooook my guess is that "inappropriate" in this context almost always means sexual. If they were just taking two hour lunches and forwarding each other joke emails on the university server, he would just come out and say it. The only other reasons to be that vague would almost certainly be worse, gun running, drug muling, dwarf tossing, etc.