Sorry if I misinterpreted your post - chest-thumping is a common occurrence and creeps into many threads.
As for moving vs not moving - threegun makes some very good points about your reaction having a lot to do with where you are in the reactionary curve. If BG has the draw on you, then you're probably more inclined to get the hell out of the way rather than try to draw. If both of you are drawn, then the situation changes slightly.
I can tell you that standing there pointing your weapon at someone who has their weapon pointed at you and NOT getting out of the way will set off every red light and siren in your head. Your brain is going to ask what the hell is wrong with you and why are you still standing here?!?! A person's natural reaction is going to be to get off of the line between you and BG.
It takes a LOT of practice (not to mention mental preparation) to train yourself to face down a drawn gun. It just is not the smartest place to be. Another point is that your body is going to want to do things all by itself once it realizes that you're being shot at - and standing still is not going to be one of them. Takes a lot of time to train yourself to overcome those natural reactions. Contrary to what some people think, your brain reacts poorly to the chance that it might take a bullet.
I think threegun made the point that if you are AHEAD of the curve, then BG should never get the drop on you. If you are BEHIND the curve and BG already has the drop on you then you're going to get the hell out of the way. And if you're IN the curve then it's going to be a split-second tactical decision - and your brain normally reverts to muscle memory or instinct during that time.
I think an important thing to remember is that this REALLY isn't about whether or not you "move", but whether or not you attempt to disrupt the BG's ability to maintain SA/SP. Average CCW'er isn't going to be running around with his/her weapon at the ready, so already you are that much further behind the curve right out of the gate.
Even those of us that have been trained and have operational experience will tell you that standing there looking at someone level a weapon at you is not a natural thing to do - and WE have our weapons AT THE READY. We are trained to shoot someone with a weapon as soon as we have a target, so we STAY ahead of the reactionary curve and maintain the advantage. Unless you have trained in this manner or train yourself to react this way, you are probably not going to maintain POA/POI hits under high-stress. I don't have a report to point to, but I do have operational experience - FWIW. However, I've seen many people (on both sides) react to being surprised by moving out of the way. Whether that's ducking behind a dumpster or just a lateral step it's all the same, and your reaction is going to have a LOT to do with your training, or lack thereof.
What I've seen the most of, and what has worked for me, is to simply drop to the ground. You present a much lower profile and it is a much more natural reaction. It's also fairly easy to complete your draw and acquire a target, especially if you practice it.
Pick a few movement drills and see if they work for you. Like I've said in previous posts, it's not going to be something you have time to think about, so practice it extensively and then find somewhere to practice it for real. See what works for you.