Firing Fulmer was NOT a mistake. How he was fired, when he was fired, and who he was fired by, was a mistake. I know from people who have worked under the the last three HCs that Fulmer had let the program slide in so many ways. Lots of issues beyond just wins and losses. The hiring of Hamilton was the biggest mistake. Fulmer is the alpha point on the current state of the program. The worst 5 year period of UT football since 1909 starts with Fulmer's 5-7 debacle. Saldy, the fate of the program was in the hiring decision made by Hamilton. When you think of the what ifs regarding who UT could have hired it is more than depressing.
Look at Alabama. How in the world did they end up with Mike Price, as a choice? How does LSU go 20 years with coaches like Denardo and Hallman? And keep in mind that before Bama got Saban they had already hired Rich Rod, when he had a change of heart and stayed at WV. It wasn't till then that the Bama folks ponied up the $$ to get Saban.
My honest assesment is that UT will not make a good hire. The candidates just don't seem legit. Stoops leave OU? Aint happening. Do you think Fisher will actually leave the fertile recruiting grounds of Florida? No. Doesn't appear that Patterson, or Peterson are cultural fits, and don't seem to be persuaded by big money.
UT will get out of the cellar, but the next coach will not last more than 5 years.
UT missed the right hire 5 years ago. Kiffin was wrong for so many reasons. But, the big setback was the worst possible timing, and I don't think even Hamilton hires Dooley if the timing wasn't what it was.
Maybe you are right and TN will get a good coach this time, better then Fulmer (although I doubt we will see he duplicate Fulmer's record). That said, I would guess we would get a more motivated Fulmer this time and sure I would still bet on Saban, but Fulmer can get wins like this, we know this.