I also want to add that Bellichek's first year with the Patriots led to a 5-11 season. So if the system was perfectly set up for him, why did he fail so miserably that first year?
I can explain why the Patriots had much more success the next season. It's simple; Bellichek opened up more to his players and they finally bought into his system. Bellichek never demonstrated any emotion at all, even his notorious cockiness that he demonstrates now. Back then he was a quiet hermit who stuck to himself.
In 2001, he finally showed some emotion by predicting they would win and by standing by his players. It created instant chemistry on that team and they bonded.
The evidence speaks for itself. The patriots started the 2001 season 0-2. By mid-season, they were 4-4, which is hardly indicative of a team that is going to win the Superbowl. They lost only one more game the rest of the season. So it was obvious, something caused a spark mid-season and that was Bellichek when he went off on that rant to the media. That caused his team to finally start buying into his blue-collar "the world is against us" attitude.
If Bellichek had not started showing some emotion and opening up to his players, they would have continued down the Cleveland Brown path.