Scoring a run when 3rd out is recorded at first on missed 3rd strike

Question
The situation is 2 outs, 2 strikes on the batter, runners on 2nd and 3rd. The pitch is in the dirt and the batter checks his swing. The home plate umpire calls "ball". The runner on 2nd had drifted a little too far off base and on the check swing, the catcher comes up throwing to 2nd. As the runner from 2nd is in a rundown, the runner from 3rd scores.

When the play is over, the base umpire is asked if the batter swung. He says that he did, and then the defense runs off the field. I understand that as soon as the batter walks out of the home plate area, he is considered out, just as if the defense had thrown to 1st base to get him out after it was ruled that he swung at the ball in the dirt.

My question is, does the run count?

Answer
Tom,

The umpire missed this.  He can't make a call after the fact - he ruled that it was a ball during the play, so the run down and resulting play should stand.

Run counts because the run scored before the third out was recorded.  The batter leads off the next inning.

Brian