This Bothers Me, and we Won! (Hands part of bat again.)

[tarheelcoach]

This happened in the Mets/Orioles game last night. The ball was originally ruled a foul ball, and as the training staff attended to Melvin Mora's hand (ball hit it) the umpires conferred and changed it to a strike three. Mora argued and could be seen pointing to the bat, like it hit both the bat and his hand. But I could not imagine a scenario where it would hit the bat FIRST then his hand. It would have had to be the other way around, and so the changed call was correct. I also can't imagine a simultaneous hit of hand/bat, since the hand is on the bat, not even with it.

Am I right? If the ball hits the hand AND the bat, it has to hit the hand first, right?