Misapplication of rule???

[Manny A]

Ok, so the PU screwed up initially by telling the coach that the runner missed the base. He should've kept that to himself. Since the runner passed home before the third out was recorded, then the PU should've answered the question, "Does the run count?" by simply answering "Yes, she reached home before the third out."

Now comes the question that I'm not sure how it's handled in sanctions that allow dead ball appeals. I know that in baseball where only live ball appeals are allowed, a runner can correct a running mistake after three outs are recorded and before a "live" fourth out appeal is attempted. So in this play, if the catcher had said, "Throw the ball home! He missed the plate!", the runner can hustle back to touch home to negate the appeal.

In softball, however, I'm not certain since we do allow dead ball appeals. The new rule in NCAA play about when dead ball appeals can be recognized--as soon as it's clear the violating runner has demonstrated no intent to fix a mistake--would support an out call here if the defense announces that they saw the runner miss home. But I don't know how that's handled in NFHS or USA, where supposedly a runner can always correct a mistake until she enters DBT.

I also don't know if softball allows for continued base running to correct mistakes after the third out of the inning is recorded. So the fact that this runner passed but missed home on her way forward before the third out, but then returned and corrected her mistake after the third out is called, does that constitute a legal touch of the plate to avoid the fourth out appeal? Or can the defense still request a dead ball appeal to nullify the run?