ASA rules do note that "the hands are NOT part of the bat".
It's not possible to have a legally batted ball unless the ball was put into play with the bat (not the batter's hand).
You can't have a foul (or, for that matter, fair) ball when the ball was not legally batted.
Anytime a pitched ball touches a batter, it is an immediate dead ball.
Anytime the batter attempts to strike a pitch with the bat, but fails to put it into play, it is a strike.
Put 'em all together...what do you get?
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