You are correct, but the analysis is valid:
1st and goal on the 5, ball is snapped at 1:06. Pete plays chicken with Belichick, let's the clock run down to 26/25 seconds before snapping the ball. With Bill being cool and knowing they are prepared, he doesn't call the time out and we know the result. If Carroll had them hustle up to the line, he could have run the ball on second, got stuffed, thrown it on 3rd and then run anything on 4th. It wasn't the worst call per se, but certainly mismanaged by the Seahawks and Pete. When the Pats made the defensive subs, the move should have been an audible by Wilson, saving the time out. At the least, he could call time out with 18-20 seconds left after second down. If Wilson recognized the package on 2nd down, doesn't like the look, he can burn the time out there, and then deal with the fallout. A lot to ask a guy at that point in his career, to be sure. Regardless, the Pats were the better prepared team and it showed in the final result.