I think Barkley talks too much, in general.
But, I do think there is an element of truth to what he is saying, that goes beyond the Pats: New England/Boston teams have had a remarkable run the past decade and a half.
Since 2000, the Red Sox, Bruins, Celtics and Patriots have each won at least one championship, and been contenders in many other years. The Patriots more so than the other three. This isn't something to do with the fanbase, but rather the fact that all four teams have good things going for them at roughly the same time. It is a rare, rare thing.