I think this whole discussion is pretty interesting, and everyone has some valid points. I always have felt there are three primary factors that will determine a teams record and success, with a few lesser components. It's like a pie sliced into four equal parts. One slice is personell decisions, including the draft, FA, who to resign or release, etc., this gives you the talent. Another slice is coaching, and coaching decisions such as big tent issues like what type of defense to run down to the in game descions, and being able to get the best from each athlete. The third slice is injuries and general luck. Injuries are a part of the game, but can really devastate a team if it hits the wrong person or position. Luck is that bounce of the ball thing. Or maybe a bad call goes against your team. Some days lady luck might be shining on you, and some days not! The last piece are the complimentary components all put together - this would include the ownership, the fan base, the history of the team, and a whole host of other minor things.
I think in NE's case, coaching played a huge part. I think they maximed every piece, and every person to their fullest, and put them into the best position to win. The other three components also played a heavy role, with excellent drafts and personell decisions, a great ownership group, and lady luck smiling on them as well.