When the UNC Notice of Allegations hit the public, one question was batted around a lot, mostly by State fans and national media types: How does Butch Davis still have a job?
UNC's defense is basically that Butch Davis didn't, and couldn't be expected to, know about John Blake's side job, or a rogue academic counselor, or the various trips and benefits players accrued on the side. The football program, according to UNC, did due diligence in informing players what was and wasn't allowed. To fire Davis now would put a lie to that claim, and send up a big red flag to the NCAA's committee in charge of determining the penalty.
That's the risk in firing Davis. What's the risk in keeping him on?
Well, the immediate danger is that the NCAA doesn't buy that Butch Davis was unaware of everything going on, and punishes UNC more harshly for protecting him. This doesn't seem likely, of course. One of the first things passed around about the NoA was the observation that Davis's name doesn't appear once; he and the university have cooperated fully and even queried the NCAA in advance about hiring Blake. They appear to be cool with him.
Looking long term, Carolina is going to hit with sanctions, most likely loss of scholarships with a decent chance of a year or two of postseason bans. This leaves two problems for Tar Heels. First, they've got to rebuild a team under those recruiting limitations, which likely spells a few years of sub-.500 seasons. And second, you've got the guy who presided over this downfall running the show. It's a disadvantage in recruiting, when other teams can point to the danger of having your wins vacated or your postseason plans dashed should you attend UNC. It brings extra scrutiny and suspicion on everything that happens in the program. And it alienates a portion of the fanbase. There's always been a vocal minority that hasn't been happy with Davis, going back to his pay raise after his first season. Tar Hee fans have always prided themselves on UNC running a clean program, and some won't come back as long as the guy in charge of the current spate of embarrassments is still around.
UNC is betting that this group is small, and can be lured back with a stretch of success in a clean-run program. I bet they're right about the former and wrong about the latter; people hold grudges. But if Baddour and Thorp have determined that Davis did the right thing, it'd be wrong to cut him loose just because of the outcry. But it's still a risky position to take.