Rex's "I'm Better Off Fired" Line was a Dogwhistle to other potential HC's
He strategically let this out to the media for other Head Coach candidates to hear, to let it be known that the offensive problems were Tanny's but especially Woody's for not shoring up the offense with better players. It's hard to argue that the offensive players were mostly completely offensive and there had to be some backroom machinations for that to have happened - beyond Rex's control.
So he's dogwhistling to other coaches warning them to reconsider an offer Woody (or new GM might make) because they won't have anything to work with either. Sounds like he's fighting for his job.