third stike...not dropped

Question
Runner on 3rd, no outs.  On a swinging-missed third strike that the catcher obviously catches, the third base coach yells at the hitter to run to first base...drawing a throw from the catcher.  The runner scores from third.  Is this runner interference according to rule 8, section 7, rule P? "A runner continuing to run and drawing a throw will be considered a form of intereference".  Should the runner be out at third also?

Answer
Hi Ted,
sorry to take so long I was out of town for a couple days.

I know what I would do BUT I want to give you the best answer possible.  I have a friend who had the dish in the women's college championship game a few years ago.  I emailed your question to him for his opinion.  Please give me another day or so and I'll get you a definitive answer.
thanks
Mark

Hi again Ted,
based on your question here is the answer Bryan gave me

Hi Mark,
     It sounds like to me that this is a planned play by the coach to get the throw.
I would rule that we do have interference on a player already put out so now we have the runner closest to home also out which would be the runner from 3rd.
     When you make that call be ready for an argument, but the coach won't do that again for a long time.
Hope that helps,
Bryan

this is very close to my original answer, if there is absolutely no question that it was a swing and and a catch.  I was thinking I might eject the coach for unsportsman-like conduct or making a travesty of the game.  I would make that decision based on "being there".

Hope this helps
Mark