Do you count the run?

[mcrowder]

Further, (and I think I'm still on the same page with Tim here) I would further assert that the R3 would not score if the BOOT appeal out were only the 1st or 2nd out of the half inning rather than the 3rd out.

This is the only part of what you said that I would disagree with. If R3 scores on a passed ball and is NOT forced home, he is not scoring BECAUSE of the improper batter's time at bat, but rather because of the passed ball. But I also acknowledge that the various powers that be differ in their opinions of the handling of this sitch.