Tag up DP, does the run count?

Question
Question
Bases loaded, one out, fly to deep outfield for second out, all runners attempt to tag and the runner on third scores, but the ball is thrown to second before time is called since the runner left early.  

Ump calls the runner who started at second out for leaving early, but says the run counts.  He called it a "live ball" appeal and said that it is a timing play, so the run should count.  Do you agree?   Please explain.


Answer
I do agree.

The only time you are not going to count the run is if a runner that was forced to advanced is put out for the third out.  The runner on second was not put out with a force out.  

Even though it looks like a force out, a runner that is put out on appeal for leaving early is not a force out. That runner was not being forced to advance.

So what you have here is caught fly ball for second out, run scores, third out recorded on an appeal of a runner leaving prior to the ball being caught.

This is just like any other third out that is not a force out being recorded after a run scores.