That was a large part of it. Forcing turnovers is a skill, so they get credit for that. Recovering turnovers is the most random thing in the game of football other than the coin toss. So luck is involved there.
I am not saying Belichick isn't great. But miracle worker makes it sound like he created a brand new offense for the 3rd string guy to run in a week. He did not such thing.
He gave him a limited number of plays and had his other two units step up. And the Texans were the perfect opponent.