I hate to nitpick, but the defense reacted to the play, that's why they sent Butler out at the last minute when they saw 3 wide receiver package on the goal line. It just so happens Carroll chose the play that was most successful for them on the goal line and the Pats had picked that up and practiced it. And the Seahawks were right, it was a high percentage play. If it was anyone else other than Browner on the line against Kearse, Butler would have been rubbed and the Seahawks would have scored and probably won the Superbowl that year.
The stars aligned perfectly that day.
You're right, the corners were based on the number of receivers the Seahawks sent out, but I still think Belichick baited Carroll into throwing the ball and they had Avery good idea what they would run and we're ready for it.