Hit by Pitch Rule

1.) The USA Rulebook states (Rule 7, Section 1, Art. F): The batter becomes a batter-runner when a pitched ball, not swung at nor called a strike, touches any part of the batter's person including the hands or clothing. The batter's hands are not part of the bat. Effect: The ball is dead and the batter is awarded 1st base. 

EXCEPTION: If no attempt is made to avoid being hit, the batter will not be awarded first base unless it is ball four.

2.) Rule 8-1-F states: The batter becomes a batter runner when a pitched ball, not swung at nor called a strike, touches any part of the batter's person including the hands or clothing. The batter's hands are NOT part of the bat.

 

To be clear, if a pitched ball touches a cleat, jersey, batting helmet, etc, That's a "Dead Ball," batter is awarded 1st base. A key word in this rule is "not swung at."

Hit Ball Hits Runner Rule

1.) Rule 8, Section 7, Art. J: The runner is out when the runner interferes with a fielder attempting to field a batted fair ball or a foul fly ball. Effect: The ball is dead and the runner is out. Also, the batter that hit the ball goes to 1st base.
 
Regardless if you feel the runner did it on purpose or not, the runner prevented the fielder from making a play by getting hit with a batted ball. Ball is dead, runner is out!
 
Please watch this YouTube video and start it at the 10 second mark: MLB Runners Hit By the Ball - YouTube This is 3 minutes of footage of Major League Baseball runners getting hit by a batted ball. If you notice, every single one of these plays, the runner prevents the fielder from making a play. Every single example here, the runner is out and the batter is awarded 1st base!
 
2.) Rule 8, Section 8, Art. D: The runner is NOT out when a runner is hit with a fair untouched batted ball that has passed an infielder, excluding the pitcher, and in the umpire's judgement, no other fielder had an opportunity to make an out.
 
There is a key word in this one... "A batted ball that has passed an infielder."
 
So think of it like this. You have a runner on 1st base and the batter hits the ball. The ball first passes the 2nd baseman and THEN the ball hits the runner. You have a LIVE BALL. As an umpire, you call nothing. The 2nd baseman had their opportunity to make a play and they messed it up. That's not the runners fault. That's the fielders fault. Don't punish a runner because a fielder messed up. 
 
Here are two YouTube videos that describe this: Ball hits runner behind fielder - YouTube (really focus on the 1:25 mark) and Deflected Batted Ball Hits Baserunner - YouTube