If you're Nutt and you compare your situation at Ole Miss to the situation at Auburn, it's a no brainer.
At Auburn, you have Bobby Lowder all but controlling the university. You have to compete directly with Nick Saban and Mark Richt in your two rivalry games and also in most of your recruiting battles. And on top of that, they're going to expect you to win and win big immediately, along with the expectation that you have to beat Alabama more than not. They fired a coach that won an average of 10+ games a year for 4 years because he had one 5-7 season.
At Ole Miss, you have a school that's going to its first bowl in 5 years (and you are the one that led them to that bowl). Yes, we fired a coach after one losing season, but you could argue that we've been humbled by the Orgeron tenure. Your in state rival is in flux right now between coaches, and you just beat them 45-0. The fans have chanted your name multiple times after wins, and you just bought a bid farm and transplanted your entire family a year ago. The downside at Ole Miss is Pete Boone, and I'd argue that the administrative situation at Auburn would be as bad, maybe worse, for different reasons. Sure they could probably pony up more money, but why would they pay big bucks for another Tubberville? And even if they did pony up major money, it's not exactly like Nutt is starving. He's been making great money for a while now.
I'm also pretty sure that Nutt and Tubberville are decent friends, so I'm sure they talk. If Nutt would even consider Auburn, I'm sure he'd talk to Tubby first to get an idea of what the situation is really like.