They don't "resign." That is just how it is couched for legal purposes, etc.
He was told to "resign" or "be fired." There was not a choice. This wasn't Gruden feeling remorseful and humbly resigning because it was the right thing to do. Not a guy like him making $10M a year. He had a proverbial gun to his head and pulled the trigger himself instead of having his boss do it for him.