Reader Brian Rodriguez makes a good point about on-deck batters sometimes becoming part of the game:

something just struck me while watching the replay of the dodgers/royals game from thursday. as adrian beltre came home with the go-ahead run on cesar izturis's base hit, vin scully (interestingly) pointed out how on-deck hitter kevin brown was telling beltre not only to slide, but in which direction (away from the throw). what struck me was, what's the on-deck hitter doing up there might in the middle of the play? i know this happens all the time and i'm sure it's nice and legal, but it seemed odd how someone who has no part in the play just jumps into it like a "home base coach."
thanks for being my sounding board
brian

Hi Brian,
Actually, there is a rule that covers this. It does not refer to on-deck batters sepcifically, but...

7.09
It is interference by a batter or a runner when: (e) Any member or members of the offensive team stand or gather around any base to which a runner is advancing, to confuse, hinder or add to the difficulty of the fielders. Such runner shall be declared out for the interference of his teammate or teammates.

and

7.11
The players, coaches or any member of an offensive team shall vacate any space (including both dugouts) needed by a fielder who is attempting to field a batted or thrown ball. PENALTY: Interference shall be called and the batter or runner on whom the play is being made shall be declared out.

Directing the runner to slide away from the catcher as he is fielding the ball, I would consider adding to the catcher's difficulty. They would only call it if the player interferes with the play (which never happens).
Given that there are rules prohibiting certain actions by the third-base coach:

7.09
It is interference by a batter or a runner when: (j) With a runner on third base, the base coach leaves his box and acts in any manner to draw a throw by a fielder.

It is odd that the on-deck batter has carte blanche to hang out around home. It's a good point--we never question it because it's so common, but why allow it? Why not let a coach from the dugout wander out and direct the homeward-bound runner? We not let his wife on the field to plant a big kiss on him after scoring?