Now, maybe I'm joining Adam in a windmill-chasing excursion, but I'm leaning towards agreeing that the illegal touch caused the ball to become dead immediately, therefore the clock should not have started. If I remember right, one of the rules fundamentals is "The official's whistle doesn't cause the ball to become dead; it is already dead."
Try remembering rule 5-9-4 instead. You're treating it as if it doesn't exist.