Protest question

[Coach&Blue]

I am a manager of a team. We play Major (American) League Rules. My hitter had a 2 - 2 count with 2 outs and runners on 1st & 3rd. By batter hits a line drive to LF for a base hit. My better, on his back swing, dropped the bat and hit the plate umpires leg. He yells "Dead ball, Batter is out for hitting me with the bat." He stated to me that he has a personal rule that if he gets hit with the bat he is out. I of course protest the game. Will I win this protest? I never heard of any rule where the umpire can call a batter out for getting hit with a bat or a rule where the umpire can use his own personal rules. There was no warning, and it wasn't on purpose. The bat didn't hit him hard or anything.