Boise coaches haven't fared well in the big leagues. The most successful ex-Boise coach is by far Houston Nutt.
Sorry, this generalization is way too overblown.
1. Yep. Houston has been their most successful ex-coach.
2. Dirk Koetter won between 8-9 games a year at Boise. He goes to Arizona State who, with an exception of one or two years, had been a 6 win team at best for 10 years. He wins mostly 7, 8, or 9 games a year there. He wasn't perceived to be an elite coach, which is why he got hired by Arizona State instead of Oklahoma, Florida, USC, or the like.
3. Dan Hawkins stepped Boise's program up. They won about 10 games a year (82%) during his tenure. He was seen as a good coach. His biggest wins were over TCU and BYU. He went to a mediocre program who was about to get worse due to a "scandal." He jumped at this opportunity, despite it being almost set up for failure. He leaves his OC who ran his elite offenses to coach Boise.
4. Petersen takes Boise to a completely new level. He wins 12 games a year (92%) during his tenure, thus far. He is not seen as a good coach. He is considered for every elite job that opens up. His biggest wins include Oklahoma, Oregon (twice), and Virginia Tech. He wins the Fiesta Bowl twice. While people rightfully knock Boise, almost all viewers respect Petersen's approach to the game. He fields potent, efficient offenses despite having mediocre talent. He fields stingy defenses. Yeah, he plays in the WAC, but so does every other team in the WAC, of course, and so did his predecessors. He's done better than any of them by a long shot.
Boise stinks as a program. I don't like them. But, it is short sighted and foolish to say that because Dan Hawkins and Dirk Koetter failed that Chris Petersen will too. If he goes to the right program, there is no reason he shouldn't succeed.