baseball rules

Question
bases loaded; full count on batter. two outs. runner on 2nd base knows he is going on anything.  Pitcher throws ball 4.  runner on 3rd base starts slowly walking home since he knows it is a free walk.  runner going from 2nd to third in his excitement rounds third base towards home.  Catcher sees this and throws the runner out.  THis is the third out and the original runner from 3rd has not crossed the home plate to score. Does the run count?

Answer
I am not sure on the ruling. For that to happen alot of people would have to alot of things wtong. First of all with 2 outs and bases loaded the runner at third would take off running wide towards homeplate not walking toward home
Secondly the runner at second would have to start running as fast as he can and the base coach would have to be sleep and not stop him on the bag. Thirdly the catcher would have to be holding the ball instead of throwing it back to the pitcher. So alot of people would have to do things wrong inorder for that to happen.

Any third out recorded before a runner crosses home plate would neglect the run trying to score.
Did this happen in a game you attended?