Obviously it isn't all luck, but it does indeed have a component of that. I'd rather stop teams by forcing punts, than by forcing turnovers, because when you face good offenses, odds are, you won't take the ball away frequently. Can't complain about the way they've done things the last couple of weeks, though.
Well, if you'd rather not instantly turn games around, you might consider rooting for another team (just kidding, to make a point). What team have you been watching the last decade or so?
Are there not good teams in the Playoffs and Super Bowl? Sure, the ball takes funny bounces, but to think it is luck that we have huge advantages in turnover ratio all our best years is to miss the point of Belichick defenses, when they are working as intended.
We lament the couple receptions allowed on a drive then cheer the "lucky" interception that is really the result od a designed play and probably part of a scheme set up throughout the drive. Even the announcer noted the "bait" play Arrington ("I think") set up so Gregory could fly out of nowhere for the easy pick.
Tacklers practice stripping the ball and the offense practices holding on at the same time, every practice, more than anyone else, I'll wager. This is and has been our defense. It is not designed to minimize yards allowed on the stat sheet, it is designed to maximize our scoring opportunities and minimize those of the opposition.
Check out how many turnovers we've forced in successful playoff and Super Bowl games. It directly contradicts what you've stated as fact about "big games" and turnovers.
"Luck is the residue of design", the saying goes and it has never been more true than in Belichicks defenses.