So "straight into the ground" is any program that does not win the CC in the toughest conference in the country, BCS bowl games, blow out top 25 teams, or have a perfect bowl record, eh? I would guess most programs don't have such extreme expectations or have learned (see Notre Dame, see Nebraska) to temper them in the modern era of the talent-rich programs harboring elite coaches and recruiters.
And how many SEC Championships during that "glorious span"?
None from 2001 to 2008. Same is true for 8 of the 12 SEC teams. Appeared 3 times. More than can be said for half the league.
BCS Bowl wins?
None. Only the teams that have won SEC championships have won those games, and only LSU & Florida have won more than 1.
Record against Top 25 teams?
Against top 10 teams: 4-11. Against teams ranked between 11 & 25: 12-13. Both pretty typical numbers for a team with an average ranking in the 15-20 category this decade. Wanna guess the win rate of EO at Ole Miss, or Monte at NC State, their respective HC gigs? Maybe LK at the Raiders? On-field coaching wasn't the problem; managing to recruit against the likes of UF, Bama, Georgia, LSU and the like without a regional talent base is. No team in the country has broken through that barrier this decade.
Bowl record? (isn't that where we measure "national prominence"?)
From 2001 to 2008, went 4-2, going 3-1 against ranked bowl opponents. Played on New Year's Day 4 out of 8 seasons, going 3-1 in those games. The record speaks for itself , Fulmer probably cut these guys off in traffic somewhere .