Actually, no they don't. I didn't know this, but the balls are inspected two hours before the game to ensure they meet specifications. I guess dimensions and inflation level are both checked. These balls were inspected and met the requirements. Subsequently, in the two hours after the inspection and before game time, 11/12 balls of the Pats were deflated. Throughout the game when the Pats have possession, one of their 12 balls is used, and when the Colts had possession, one of their 12 balls was used.
The deflation was so much that a linebacker from the Colts, after intercepting the ball, noticed that something was "wrong" with the ball, and asked that it be checked. That's what got the ball rolling in the first place.
While I don't have a horse in this race, if deflating the ball didn't have a big impact (which apparently it does, especially when cold), then no one would have bothered. The Pats cheated, and got caught. I suspect they're going to be significant consequences, such as loss of draft picks, fines and/or suspensions.