Oneil had really established UT as a strong recruiter. He had a huge fallout with Dickey over personal issues and the red-shirting of Isaiah Victor, and left. He later hinted that he made a mistake.
Green was the result of a bungled search. UT wiffed on some names that are huge now, such as Bill Self, who I believe was at Tulsa at the time. There was also the Stallings screw-up. And I think UT made a joke of an offer $$ for Barnes who was at Clemson at the time. They thought Stallings was hired, and apparently the AD made a last second play for Tim Floyd, which Stallings found out about and told UT where to shove it. UT was then left scrambling and had to hire Green, whose record was, well,... average. He was a decent coach, but had never done much to wow anyone, and on top of that was already up in years.
He did have a decent staff and a pretty good offensive philosophy. But the main thing is he inherited CJ Black, Hathaway, Victor, and Tony Harris among others. Green recruited decently and got Slay and Yarbrough. People were elated with 20 wins, but Green underacheived considering the talent. Green had never sniffed that kind of success in his previous coaching career. The comments he made about the fans has already been covered.