Here is running list of common umpire myths. Check back for updates.
The hand is part of the bat - Not true, the hand is part of the player. Anytime a pitched ball hits the batter's hand and the batter did not swing the bat and the pitch was not in the strike zone, the call is hit by pitch. If the batter does swing the bat and the ball hits the hand, the call is a strike and the ball is dead, similar to a foul tip. However, if the hand hit ball occurs with 2 strikes, the call is out strike 3 and the ball is dead.
A runner standing on a base gets struck by a batted ball, therefore he's safe because he's standing on the base - Generally this is false as the bases are considered part of fair territory and a runner getting hit by a batted ball is out for interference and the ball is dead. The only exceptions to this would be if the ball had gone past a fielder already. For instance, if the runner was on third base and the 3rd basemen was playing in, the runner hit by the ball would not be out and the ball is in play. The other exception would be if the ball actually hit a part of the runner, leg for example, that was in foul territory. Then the call is foul ball.
A pitcher must be removed after 3 hit batsmen in an inning - This is false. There is no limit on hit batters or a requirement to remove the pitcher when a certain number of hit batters occurs in the rules.
A pitched ball that bounces before hitting a batter is not a hit batsman - This is false. Any ball that hits a batter whether it bounces or rolls before getting to the batter, is a hit by pitch. In these cases like any other pitch, the batter can not intentionally try to get hit.
Tie goes to the runner - This is false. Technically there never really are any ties, as the runner either beats the throw or he does not. But for those of us without instant replay on bang-bang plays, please remember that the rules clearly state that the runner must beat the throw to be safe.
There is also an excellent list of additional umpire rule myths here: https://www.llumpires.com/rules/myths.html