My CHL instructor and neighbor is pretty experienced. He's worked for DEA in South America 25 years, worked for Blackwater in Iraq, and a bunch of other stuff. One point he hammered home was that in a face to face gunfight situation, you will, as has been repeated here, follow your training.
I've shot in Steel Challenge and IPSC back in the old days, and yes, there's some stress, but it's NOT the same as a real life encounter. Focus here a minute:
You see the bad guy. You see a gun in his hand, the hammer back, his finger on the trigger. He sees you. He raises his gun as he turns in your direction. In the next half-second, you are probably going to die.
Now, in THAT SPECIFIC situation, at THAT specific moment:
Your brain will shut down. You will NOT think.
You will stop breathing.
Your vision will narrow, and it will be difficult to scan your visual field and focus.
You will hear sounds and voices if they are present, but you will not be able to mentally process them.
Your body will stiffen, and your conscious control of your muscles will be dramatically reduced.
Your pulse and blood pressure will instantly skyrocket.
Now... in THAT state... in THAT half-second... what are you going to do?
This is where the "muscle memory" comes in that others have discussed here. You will do whatever you have trained to do. If you have practiced instantly draw-and-firing with an empty gun thousands of times until you can do it without thinking, as an instant, automatic reflex, then that's what you will do here, and you might survive.
If you slowly draw, get in position, use the Double Reverse Jivaro Thumbnail Grip, and line up the front sight with the seventh ring of Saturn, then that's what you will do here, and in half a second you will have a bullet passing through your body.
Sure, all that competition and target shooting gives you good basic skills, but in addition to that, you need to practice your automatic reflex combat response. Over and over and over. I know several instructors who do this; every morning they quickly draw-and-fire 50 to 100 times, every day, without fail. They have it down so instinctively, they can repeatedly draw and fire while reading the newspaper, or discussing the economic impact of the Civil War after 1865.
That's what will save your life if you're ever in a split second scenario like the one described.