Belichick really engineered at least 2 or 3 of those 6 SBs. By the same token, he lost the one against Philly. Then again, Brady had a couple of rough SBs too. So, sure, Brady is responsible for winning 3 or 4, but Belichick was the key component in 2 or 3.
I always say that fans who denigrate Belichick for not winning without Brady are not making an honest argument. I mean, look at the last Super Bowl. A team that averaged 34 ppg scores the lowest amount in Super Bowl history? That was a Belichick special.