I half agree, half disagree.
Look at Florida State. They kept Bobby around for what felt like forever, even though they probably should have cut ties sooner. And as a result, they fell out of relevance and were pretty mediocre for a time. They are back now, though.
Our mistake was not grooming a replacement for Fulmer, like Jimbo at FSU. We could have handled it better, maybe eased him out the door instead of just firing him the way we did, but we should have had someone ready to step in. Because if Fulmer wasn't fired then, he would have been soon. We butchered that pretty badly.