It is true (all codes). The D can still play on the B/R before he reaches 1st base, even after the third out.

I think MD Longhorn is correct now. The BRD referenced Hopkins, Fetchiet and Fitzpatrick in 2001 as agreeing to the interp which as you and Childress say, doesn't make sense.
My 2012 Wendelstedt Umpire manual reverses that interp and does not allow the BR to be put out if the defense played on somebody else for the third out. They say the defense had the opportunity to make the third at 1B out and was not vigilant.

Does MD Longhorn have other cites for this?

But the BR, having not yet reached first, is not required to continue running after the 3rd out is made elsewhere.

You would think so - but that is contrary to three official rulings (FED, NCAA & OBR) that say the B/R can still be put out for the advantageous fourth out. Now umpjim says the Wendelstedt manual says otherwise.

Carl says he hopes this never happens in any of our (and his) games. I share his wish.

And J/R agrees with the three official rulings: the advantageous 4th out applies to any force out or the B/R.

If you think this ruling doesn't make sense, ask yourself if Wendelstedt's alternate ruling (4th out is only effective if an appeal is upheld) makes sense. Bases loaded, ball to F6 who tags R2 after R3 scores. According to the Wendelstedt interp, if the B/R deserts, or R1 abandons before reaching 2nd, the run scores, and there is no advantageous 4th out. But if the B/R or R1 continues to advance, and misses the base, now a 4th out can supersede R2's out. IMO, this is the interp that doesn't make sense. Why is abandoning /deserting OK, but missing a base is not? Neither act is legal base running.

Instead, if we believe (as has been officially ruled) that a 4th out is effective whenever a forced runner or the B/R is put out before reaching their advance base or if a missed base appeal on such a runner is upheld, then the rule is self consistent.

I've never bought into that theory that runners should continue running after a third out is recorded. After all, OBR 5.07 is pretty clear, in my mind, of what happens:

"When three offensive players are legally put out, that team takes the field and the opposing team becomes the offensive team."

There is no requirement whatsoever specified in the rule that says other runners are required to continue running after "three offensive players are legally put out" to meet whatever obligation they had before that third out. It says that they simply take the field at that point, because all obligations to advance are done, finished, completed.

Obligations to continue advancing to bases after play essentially concludes are limited to when winning runs score. There is nothing in the rules requiring the same after three outs are recorded. So I have no idea why authoritative interpreters out there require runners to keep running after three outs when the rule clearly tells those runner they must now go play defense.

Um ... you're aware that no run scores on this play either, right? No need for an advantageous 4th out - the THIRD out was a force already.

That aside, insisting that runners run after the 3rd out does not make sense (and never has). The inning is over after 3 outs. 4th out appeals apply to transgressions that occurred before that third out.

The inning isn't over until no appeals are possible. Otherwise no 4th out could ever be achieved.

It doesn't make sense because it requires the offense to continue playing when there is no possibility of anything to gain and after the inning has concluded, by rule. Also, by rule, there is nothing that indicates a fourth out can be recognized on a non-appeal play.

Agree. But those fourth out appeals are on running violations before the third out is recorded. There shouldn't be any requirements for runners to continue running after the third out, per the wording of 5.07.

The onus is not on the offense to keep playing but on the defense to continue to play to get the advantageous fourth out. A good crew will continue to watch the defense until action is relaxed. The umpires can then rule if a proper appeal is made.

Wendelstedt says that the onus is on the defense to get the proper third out.

If you go with the interpretation that fourth outs can be made on non-appeal plays, then that puts the onus on the offense to keep playing.

I will agree it is on both to keep playing. The situation in the OP would require the BR to accquire 1B before the defense can tag the BR or 1B for the run to count.

This exactly.