I see it the other way actually. Fulmer went out in a bad way. I would think nothing could be better for the man then to come back win 8-10 games a year for 4-5 years. Maybe win 4-5 bowl games and then retire and turn UT over to the next guy. Tarnished, is the way Fulmer was forced out IMO.
If Chavis wanted to HC somewhere, he would have done so years ago. He has spent too much time as a DC and is hard wired in that respect. Some guy are tactical and some are strategic.