The issue is that there was already one out. The third out was the tag on, not necessarily a force, and the run crossed the plate before the tag, therefore it counts...apparently. The "4th out" was stepping on 3rd. If he had stepped on third first, and then tagged the runner standing on third, the run wouldn't have counted....I think.
It appears the ruling treats this scenario like the following:
Runners on first and third, one down. Ground ball to 1B who fields it close to the bag, he steps on the bag for the 1st out of the double play (but 2nd out of the inning). Then throws to 2nd for 2nd out of the double play (but 3rd out of the inning) which needs to now be a tag. Runner on third crosses home before the tag. That run counts.
We can all agree why this counts, the 3rd out was not a force, it needs to be made before the runner crosses the plate in order to avoid that run.
The fact that the rule book apparently treats both of these completely different scenarios the same is asinine (jeez that's a hard word to spell, two esses makes more sense).
On top of all this, the appeal process is ridiculous. There needs to be some serious adjustment to this rule already being addressed.