McCoy could have departed as well after an award-winning junior season in which he finished second in the Heisman Trophy voting.
But he said he never took the idea seriously, and last night's BCS national-championship meeting with Alabama in the Rose Bowl is why he still wears a Texas uniform.
"I'm a big dreamer," McCoy said. "I've always wanted to be in this position, and I hope to end it the right way."
It happened for Hansbrough as the Tar Heels celebrated a victory over Michigan State. A difference here is that McCoy's second-ranked Longhorns are an underdog to top-ranked Alabama.
But McCoy has accepted challenges throughout his life. The son of a high school football coach, he grew up in Tuscola, Texas, a town of about 700. When he arrived at Texas, McCoy, at 175 pounds, had more of a kicker's frame than a quarterback's. He wasn't projected as the replacement for star Vince Young. Jevan Snead was the man.
"He came in as a five-star guy and was going to be the next quarterback," McCoy said. "I had to work twice as hard to beat him out."
McCoy got the nod during fall drills, and oddly enough, it was after a loss - at home to Ohio State - that coach Mack Brown knew he had the right guy.
"He went up against Troy Smith, who won the Heisman that year, and threw a couple of interceptions and fumbled at the 5 going in," Brown said. "After the game, to see the look of disappointment on his face made me feel like he's for real, that he got it."
McCoy went on to guide Texas to a 10-3 season and a bowl-game victory, the first of 3 straight years in which he led the Longhorns to double-digit victories and bowl titles. McCoy was named offensive MVP in all three bowl triumphs.
But after three seasons, a void remained in his career. There had been no Big 12 championship. Texas tied Oklahoma and Texas Tech for first place in the South Division but lost to the Sooners in a tie-breaker.
McCoy had been everything to Texas - including an NCAA record-breaker for season accuracy at 76.7 percent as a junior - except a champion.
When McCoy got off to a sluggish start by his standards, with seven interceptions in his first six games compared with eight all of last season, Davis believed that McCoy was looking for a gear that doesn't exist.
"After last season, I called Colt in and said, 'Now, look, no one who has ever played the game has completed 77 percent of his passes like you did last year. Don't come back and think you're going to complete 80 percent.' "
But, Davis said, the ultra-competitor in McCoy took over, and the player with the super statistical season in 2008 was trying to top himself in 2009. Bad move. He started slowly, and on a night when he also battled illness, McCoy threw a pair of picks against Texas Tech, which helped keep that game close.
"Somewhere along the way, around midseason, he realized this was his last run and he was no longer going to press," Davis said. "He just had fun, like last year."
The numbers started to soar. In the final six regular-season games, McCoy threw 16 touchdowns and two interceptions. The Longhorns blew out the first five foes, then outpointed Texas A&M as they closed the year.
His latest outing ended the momentum for McCoy and the offense. Nebraska manhandled Texas in the Big 12 championship game.
McCoy was sacked nine times and got the Longhorns into the end zone just once in a 13-12 victory.
For those looking for clues about how McCoy and the offense might fare against the rugged Crimson Tide defense, consider that in the games against the Big 12 opponents with the best defense - the Cornhuskers and Oklahoma - McCoy completed 54.7 percent with four interceptions and one touchdown. For the season, he completed 70.5 percent.
"Nothing's going to be easy, I know that," McCoy said.
Davis knows from the first time he sat down with McCoy in his office, 5 years ago, that nobody on the Texas sideline is better prepared for this challenge.
"He said he was going to be the best I ever coached," Davis said.
Davis raised an eyebrow, but on the inside he was busting a gut.
"Vince Young was about to lead us to a national championship," Davis said. "We had Chris Simms and Major Applewhite, and here's this scrawny kid sitting in front of me telling me this?
"What I didn't know was how hard he was willing to work, on his game and his body."
McCoy remembers the meeting.
"He actually did laugh," McCoy said. "But he believed in me."
The rest is Texas history, almost. The most important game remains, and McCoy, who has won more games (45) as a starter than anybody in the game's history, says don't bet against him.
"Nobody's won more games," McCoy said. "But it's all about winning the national championship."