In 2003, The Patriots average win was by : 10.285 (only 1 game by a FG)
In 2004, The Patriots average win was by: 13.71 (only 1 by a FG)
In 2005, the Patriots average win was by: 7.64 (3 by a FG).
So, in the last 3 years, where the Pats have had 38 wins, only 5 of them have been by a FG. And last year's down year can be pointed to the defensive issues.
But, you're right, the Pats find themselves in a lot of close games. Granted, the the 3 SBs in the last 5 years have all been close, but even if you decide to add the last two, you still have 4 other games where the Patriots won handedly.
Yes, having Adam would be great. However, it looks pretty clear to me that he snubbed the Patriots. Not the Patriots him.