There is a study by the Force Science folks that indicates that within a short distance - trained and untrained folks have a high probablility of a hit and even a head shot. When you get to distances about 12-15 yards (IIRC), then the untrained fail to perform.
That should support DNS's statement. It was on policeone.com by Ron Avery, I think.
BTW, at high end FOFs, you see folks forgetting to breathe and turning blue or having pretty impressive parasympathetic rebounds, taking them down after a run. So that's stress in my book. I recall babbling rather inanely after one.