I agree with JB. The hallmark of the Patriots over the years is that they play very solid, team oriented football. They may not have 6 Super Bowl wins without Brady, but they would have some for sure.
Put Brady on the Jags or Browns and I think he has zero rings.
This seems right. Brady only had one season of a truly astonishing NFL offense and they didn't win it all (though 19-1 is pretty amazing). Usually, it was the whole of the team winning super bowls for the Patriots. Whether it was the first championship, or this one, it was rarely Brady dominating the competition. The whole stole the show, most often led by the defense. Where Brady did seem to excel, and perhaps shine more, was in the AFC Championship games.
Even his 4 TD game against Seattle, had 2 picks. The comeback against the Falcons occurred after an 82 yard pick six. There are more examples, where Brady has always been good, but not so dominant to carry the team.
Belicheck has brought the team with him most often. The best Patriot offenses seemed to be those in the 10 year stretch of not winning the title. The Giants upset being the biggest.
Clearly Brady is great, if not mostly for his unbelievable consistency and rare key mistakes. But, even other great QB's don't go on this type of run, with such substantial roster turnover, if the guy leading the ship isn't the greatest ever.