I think this psychological factor shows up in game days more than people want to admit. The mentality of playing the Patriots is such that you don't play as naturally and instinctively, and that's partly because they will use your nature and instincts against you. I see it on the field all the time, especially when watching other teams' DBs covering their receivers. Think "shock and awe" and how that can lead to a lack of confidence and second-guessing. Even the refs just kinda sit back in awe at times.
Belichick is an exceptional coach in this regard. He plays the meta-game.