Could you in any way invoke rule 7.02?
The runner standing on third did not legally acquire that base since he did not touch second. He could no more do that than sneak out of the dugout before an inning started and stand on 3rd hoping no one noticed. Should the pitcher give up a HR on the next pitch, the team doesn't get 2 runs because it wasn't noticed.
First off, let me remind you all that I'm definitely not the most experienced umpire on this board by any stretch of the imagination, and I'm going to explain it the way I saw it/called it, but that doesn't make it right. Now that I'm merely an ex-umpire, I can admit that.

If a runner snuck out onto the field and stood on third base and watched a homerun, my understanding would be that I would first rectify the situation (i.e., throw the guy off the field) and then the batter would be entitled to his four bases. But my understanding is that the only way in which the homerun would not stand would be if in the opinion of myself or one of the other umpires, the rogue runner was guilty of interference.
So in your scenario, I'd deal with the rogue runner separately but would allow the result of the play to stand barring interference. I would also probably be disposed to define interference quite liberally if there were any doubt, but in the case of a ball hit over the fence, it would seem pretty unlikely.
Following that, in the comment for Rule 7.01, it states that a runner that legally acquires a base may not return to a previously occupied base. Therefore the runner now on first cannot go back there after touching second.
I think the, outside of talking to anyone else, that I would have claimed the ball was not legally in play, returned the runners to their previous bases, and ejected the manager. I would not have called the runner out any more than I would award an out for a runner that attempts to steal a base, and the batter hits a foul ball, and doesn't immediately return to his previous base. The game simply would not resume until he moved.
The problem is, the runner on first went back there during a dead ball. The ball obviously shouldn't have been put into play, but that would be akin to accidentally putting the ball in play while baserunners went over to talk to each other and then immediately calling them out for standing in such a manner that one had passed the other.
I suppose the problem is that this seems to me to be closest in the rules to a batting out of turn situation. Meaning, since the defense appealed the situation before anything other than a balk had actually happened, the runners simply get put back into the correct spots. If the runners had actually done something followed by an appeal, by analogy to BOOT there would be justification (perhaps?) for calling the runner out on the basis of the appeal, and I decided, admittedly without being too confident in my decision, that he BOOT rules were the closest ones and therefore what I should be reasoning from. The problem is, BOOT is also very clear that a balk gets enforced anyway. Hence the idea that I'm supposed to put everybody back on their correct bases (since the fielding team alerted me to the problem), not declare any outs (since they alerted me to the problem before the runners had done whatever it was they were going to do, by analogy to waiting for an at-bat to complete in a BOOT situation) and then enforce the balk from there.
The thing is, had I been thinking more clearly, you're right - as soon as I realized the defensive coach had merit, I should have decided that before the balk occurred, I got something in my eye and lost track of the play, and therefore called time. "What, you didn't hear me? Sorry, I'll try to be a little louder next time".
What was the reasoning behind ejecting the valid pinch runner? And you could likely claim a tortuous interpretation of illegal subsitution by saying the 2 baserunners substituted for each other.
This is a fun one though. I wonder if MLB has any "Ask the umpire" type of things.
The reasoning was basically that the coach had talked with all three of them before doing this, and so I was ejecting the three runners and the coach because they were all in on this and should have known better, so they were all guilty of unsportsmanlike conduct. With that said, I agree it's much more clear-cut in the case of the two people that were standing in the wrong place and the coach who told them to do it. The whole thing was a mess - you don't get into umpiring because you want to eject 13 year old kids (or even their loud, obnoxious parents).
Edit: I suck at quote tags.
Edited by CSteinhardt, 26 March 2009 - 03:28 PM.