Yeah, nobody ever wanted Rodney Garner or Trooper Taylor or Stan Drayton or Latrell Scott as a recruiter; nobody ever wanted Cutcliffe or Chavis as coordinator; nobody every wanted Brooks or Sanders as a position coach; and Fulmer doesn't have 4 former assistants as head coaches currently. (Ignore for the moment those coaches have easily found jobs at BCS schools or promoted to higher positions at other schools).
Fulmer hired coaches specific to their position -- coordinators for coordinators, position coaches for position coaches, recruiters for recruiters, and player personality managers for their specific role. He was loyal and that loyalty was reciprocated with extraordinary stability. Of course, leave it to the kiddies to twist stability into a "bad" thing.
If you like coaches who leave all the time (and celebrate it as evidence of coaches "desirability" and "superior" talent), then look at Majors' offensive runs from 1977-1988 or his defenses his entire tenure. Guess how many seasons Majors managed top-3rd SEC offenses or defenses during those years? Try zero, with the "great" staff evidenced by how many coaches left all the time.