Via email from co-worker Chet.
Although I haven't heard any trainers directly address this it has been hinted at by some:
Scientists discovered that people move faster when reacting to something than when they perform "planned actions".
In an experimental "duel", published in Proceedings of the Royal Society B, they studied the speed of these two types of movement.
...
Pairs of participants were put in a button-pressing competition with each other. Each was secretly given instructions of how long to wait before pushing a row of buttons.
"There was no 'go' signal," said Dr Andrew Welchman from the University of Birmingham, who led the research.
"All they had to go by was either their own intention to move or a reaction to their opponent - just like in the gunslingers legend."
Those who reacted to their opponent were on average 21 milliseconds faster than those who initiated the movement.
During one or more of the classes I took from Insights Greg Hamilton told the students to "use your startle reflex" when the buzzer goes off to decrease your draw time. It works.
You can actually see it other shooters. New shooters take a lot longer to start moving their hand toward the gun and it moves slower when it does move. Tell them to use their "startle reflex" and after a few repetitions you will see their hands jerk into motion and reduce the amount of time required to get their gun deployed.
Apparently we have different pathways in the brain and we can consciously reroute the signals to decrease the time.
This strengthens the wisdom taught in NRA Personal Protection courses about "drawing a line". The students are told they must have a mental threshold past which they will take some sort of action. It might be something like "the door opens" when someone is trying to break into your safe room. Or "they come around the corner of the counter" when the bad guy is advancing at you with a knife. You are reacting to something the bad guy did. In addition to increasing the speed of your response to a threat you are less likely to suffer from a "boiled frog" situation where the situation escalates and you keep postponing your response because "it's not that bad" yet.
Update: See also the Scientific American podcast via Say Uncle.