Bellicheck reputation really came from his years as the Giants DC.
While he did have a reputation then, it was pretty damaged by how poorly he performed in Cleveland as head coach. He was able to rehab it some with Parcells as his d coordinator with the Patriots and Jets, but the way he f'd over the Jets to become the Patriots head coach didn't do him any favors. The 'genius' label didn't really become prominent again until that Super Bowl win.