The only way you could get the run to score on a “timing” play is if the batter were the second out and the runner coming into third was tagged out for the third out. Then the run would count only if the runner touched home before the other runner was tagged out.
And the DP with runners retired at third and second to end the inning would also negate a run.
You know, I really enjoy this board. One of the things I enjoy is how fast replies can come back. Unfortunately, I get sloppy trying to keep up with things.
I meant to say “According to number 1”, as that is what supports my original statement. My typing skills are a bit suspect, though. Number 2 certainly applies in any instance the third out is forced.
I hear there’s this button called “Preview Reply”. I need to find it and start using it.
Related question: Is this also true in NCAA baseball? Little League? Softball? Japan?
I believe that nails it! Thanks very much (in fact, thanks to all who contributed).
Notice that there is a distinction between the batter and another player, in that the batter doesn’t have to be forced; a tag out of the batter also blocks the run, while a tag out of another runner, even if he could have been forced out, does not. I have seen that happen. What happens is that a ball is hit to the 2nd baseman who sees the runner coming from 1st and attempts to tag him. The runner stops, backs up, allows the runner from third to cross the plate, then gets tagged. Run counts. Bad play by second baseman. Now add a lazy batter who does not bother to run to 1st, seeing the scenario develop this way. The second baseman realizes his goof and tosses to the first baseman who touches first, making a fourth out (and a double play, incidentally). The fourth out counts and the run goes off the books. I have not seen this, but apparently it has happened.
In looking at the rules, I noticed a case crossing the place AFTER the third out counts.
The bases are loaded and the batter walks. One of the runners originally on first or second overruns the next base and the catcher throws the runner out, but the runner on third has not crossed the plate yet. By rule, the run counts.
Yes, because the runners are considered to have already advanced on a base-loaded walk. The walking to the base is a necessary formality. Technically, as soon as a 4th ball is thrown by the pitcher the batter is standing on first. His body just has to catch up to the rules. 
So the player overrunning the base occurs (technically) after the runner on third has scored.
Weird, innit?
Well actually, the run counts without ever crossing. Ha-ha.
To speed things up, they should just have the third base runner go directly to the dugout.
This is inaccurate. Whether the runner is tagged out or the base is tagged does not matter. If it is a force out, the defense has its choice. It’s still a forced out. Now in the above scenario, since the runner who was on 1st is tagged out (a force out), the run does not count and there are 3 outs. Inning over.
Here is a situation in which there are four outs. (I gave this before last year, but I’ll repeat it.) One out and runners on 2d and 3d. A fly ball is caught for the 2d out. The runner on third scores, but the runner on 2d attempts to go to third and is tagged out. However, before he is tagged out, the runner on third crossed the plate. Three outs and the run scores. However, on appeal, the defense tags 3d base claiming the runner on third left too soon. The appeal is upheld and the runner who was on 3d is declared out for the fourth out. This 4th out is necessary. Otherwise, the run counts.
Now, change the scenario a little. One out and the bases loaded. Fly out and the runner on 3d tags up and scores, and again the runner on 2d is thrown out at 3d for the 3d out, but the runner on 3d had crossed the plate. Three outs, but the run counts. Now, however, there is an appeal on the runner who was on 1st and tagged up to 2d, claiming he left too soon. This appeal is upheld. This is a kind of force out, since the defense merely has to tag lst base. Does the run count?
Dangit, I got here too late (call me first the next time baseball rules come up, ok?) to add anything except: it’s also true in Little League. LL uses the MLB rulebook (with a few additions). It’s probably true in all levels of baseball; I believe all organizations use the MLB book with the exception of High School ball (which uses “The Federation” rulebook), and this isn’t one of the differences between the two rulebooks.
barbitu8:
Now, change the scenario a little. One out and the bases loaded. Fly out and the runner on 3d tags up and scores, and again the runner on 2d is thrown out at 3d for the 3d out, but the runner on 3d had crossed the plate. Three outs, but the run counts. Now, however, there is an appeal on the runner who was on 1st and tagged up to 2d, claiming he left too soon. This appeal is upheld. This is a kind of force out, since the defense merely has to tag lst base. Does the run count?
I’m a softball umpire, not a baseball umpire, but the rules of both games are very similar. That is not a force out, so the run scores.
Correct. This is actually specifically covered in the “Definitions.”