Dropped third strike hitting a batter-runner.

[Illini_Ref]

This occured in a game that a friend of mine had (he had the bases).

A batter swung and missed a third strike that the catcher failed to catch. The ball came up and hit the batter. The PU said foul ball and put the batter back at bat. My buddy went in and told the PU that the batter did not hit the ball. The PU said it didn't matter!

I know that is wrong, but here is my question.

In reading through the FED rule and case books I find some contradicting sections. The pitch ends when the catcher secures the ball, the ball comes to rest, the ball goes out of play, the batter hits the ball, or when the ball becomes dead.

This being said, in the above case the pitch had not ended when it struck the batter. Therefore, shouldn't the ball be dead when it contacts the batter (or runner) (5-1-1a)? I wouldn't rule like this, but by rule I think you could.

Case 8.4.1 Situation I has a situation where the catcher chases a dropped third strike down the baseline where it is stepped on by the batter-runner. It states that if it is unintentional then the ball is still live. How can this be? The pitch has not ended and it struck a runner.

Help.