How would you call these two plays?

[IRISHMAFIA]

Originally Posted by jimpiano

Rule 7-4-h pertains to a batted ball which hits the batter directly off the bat while the batter is in the batters's box. Case book 7.4.9 pertains to the same play.

There is no such caveat in the rule.

The OP pertained to a batted ball which landed in fair territory and was touched in fair territory by the batter/runner. In both cases of the OP the ball was batted into fair territory by the batter who was then struck by the fair ball. In both cases the batter is out.

You might want to note at this point that I have yet to offer an opinion on out or foul. The rules clearly state that a batter which is hit by a batted ball still in the batter's box is called a strike, not an out. The position of the ball (over fair or foul territory) is not relevant.

That rule is a direct contradiction to your contention that "the batter's box offers no batter protection from being called out for touching a ball in fair territory".