Here's closer to the whole story:
1. Majors was mostly a disappointment at Tennessee, as it became increasingly evident his soft schedule at Pitt and Jackie Sherrill's designed defense had more to do with their national "title" than Majors' coaching acumen. Majors' blew a great era at Tennessee where the SEC was mostly down in the 80's, without divisional play, with usually only 1 ranked SEC opponent a year, and yet from 1977 to 1988 we won the equivalent of the SEC east once and the title once thanks to Florida's probation (and no title game), we were rarely a ranked team throughout any season, we rarely went to premier bowls, and went 1-13 against Dooley's Georgia, Bear's Bama and Florida.
2. Majors skirted the edge of recruiting and NCAA issues, getting us close to serious trouble (which Dickey managed to quiet, and kept us out of major problems). Then, in 1989 Majors put Fulmer in control of the offense and recruiting, and both finally found superb consistency. Fulmer was then quickly being offered HC jobs, as Fulmer was to Majors what Malzahn is to Chizik. Most quality coaches on staff hated Majors and would leave Tennessee quickly, with that instability killing our consistency. Majors got Fulmer to turn down those HC jobs by promising him he would take over Tennessee in 93 or so.
3. Come 1992, Majors has a heart attack and Fulmer temporarily takes over the team, and the team plays better with more consistency than it ever did under Majors against quality foes, with big wins as an underdog in big games. Majors rushes back from the hospital, trying to hide who the real source of Tennessee's success was, all the while breaking his word to Fulmer, denigrating the UT President as a "hillbilly," insulting random fans, police officers, and important boosters alike, demanding a big contract and long extension, while embarrassing the program repeatedly along the way before losing on the field to bad teams (a true Johnny Majors' signature was not letting a season go by without some loss to some terrible team on the schedule, and usually more than once.)
4. Fulmer received the East Carolina offer and decided it was time to bolt, and much of the staff planned on going with him, due to their like of Fulmer as well as their hatred of Majors.
5. Majors then insulted a bunch of folks on multiple occasions, and gave Dickey the reasons needed to fire him and keep Fulmer instead. Majors went on to Pitt where, sans Fulmer or Sherrill, he performed abysmally as both a coach and a recruiter. He spent the next two decades calling Tennessee administrators "hillbillies" and trashing the program on Alabama talk radio, where he remains a favorite of Bama fans (the routine and regular whippings we received from Bama under his watch helped as well.) Majors' supporters would continue a campaign to blame Fulmer for Majors' firing and would instigate various "fire Fulmer" movements for years as well as rewriting history over and over again to where many of the younger Tennessee fans who didn't live through that era don't know much of our own modern history prior to Fulmer.