Missed on Test

[BSBAL18]

I missed one question on my state exam, but I believe i am correct.

The count is 2-2 and B1 is trying to get out of the way of an inside fastball. As he tries to avoid the pitch, the ball hits his hands on the bat and the ball rolls toward the pitcher in fair territory. The correct call is:
A. Fair ball; the ball remains in play.
B. Foul ball; the batter remains at bat with a 2-2 count.
C. Hit by pitch; send the batter to first base.
D. Dead ball; the batter is charged with a strike, and since the count was 2-2, he is out.

I put A, and it was wrong, but it doesn't tell me the correct answer. i have always believed that hands are part of the bat... i absolutely would not call this a foul ball or a hit by pitch. And i hope it shouldnt be a dead ball because if so, I need to offer some apologies to a lot of teams! ha

This is not an attempt to get help with the test, I have posted multiple times on this forum and replied as well, so i hope i dont get trolled with "we arent doing your homework for you".