While I won't say you are wrong, I will say that it may be as likely a mutual parting.
- He wasn't exactly making friends with the NFL offices.
- His record wasn't trending right in many ways from acquisition to injury to QB dev.
- That whole Miami thing which IDK how to factor properly if at all.
- The shady referee work against a too small mkt team post Katrina sympathy
If they played nice, he can say it was burn out and they can salvage a draft pick rather than firing the first and only Superbowl winning coach in team history.
So both sides had some decent motivation to be professional about parting.