It helps that Bob Kraft has a lot of power in the NFL circle to make rule changes that help his team.
*Bob Kraft thinking*.....Hmmmm, iv'e a got a tall, immobile quarterback with a deadly accurate arm who doesn't do so well when he gets knocked around
"Hey Guys, let's make it so you can't hit the quarterback or touch the receivers!!"

Seriously it's a combination of all three, He's a great QB, the rules are set up for the passing offense, and he's got the best coaching staff in the league in his corner.
Think about it, Prototypical Tom Brady is him standing tall and hitting a WIDE OPEN receiver about 15 yards downfield and they are so fucking open they get 15 more.
He's not Brett Favre or Ben Rothlesburger Throwing the ball 40 yards with two guys at his feet, into double coverage and the dude makes a circus catch.
The Patriots are the best team BY FAR at getting mismatches, getting open and breaking down a defense.