And when you look at their schedule, much of their win total was inflated by a really, really poor schedule.
Between 2000 and 2005 they faced just two out of conference schools of note (Arkansas - a so-so 9-4 team, who they lost to in 2002, and Ohio State who they narrowly beat in 2005). That's it. The rest of their OOC opponents were opponents like Rice and North Texas. These were so far below the Longhorns that it was quite common to see Texas with a 35-0 lead in the second quarter. The Big 12 was not much healthier. Baylor had not risen up yet and Texas Tech and Oklahoma State were so-so. Oklahoma was the only team that had talent at a similar level to Texas, and they consistently beat the Longhorns from 2000-2004 (twice in humiliating fashion).
In recruiting, they had little competition at the time as well except for Oklahoma. The only two recruits that they lost out on were Adrian Peterson (who flipped to OU following a 2003 drubbing) and Ryan Periloux (who flipped to LSU). That's it. Throughout the 2000s, their recruiting was done in almost an assembly line fashion. UT would invite a host of highly rated Texas juniors to Junior Day, and between 15 and 20 would commit that weekend in April. Recruiting was basically done until NSD.
The move of Texas A&M and Missouri to the SEC further opened up the state to recruiting for the conference. LSU made inroads into the state, as did others. At the same time, Oklahoma State and Baylor got better. The latter, a lot better. Houston also made some recruiting inroads. This and strongly increased competition level sent Texas spiraling out of an elite state.