I see your point.
There is certainly at least one advantage many cops have, that repeated exposure to high-stress and/or threatening situations makes it easier to keep your head in such scenarios, than those lacking such experience.
On reflection though, it would seem that comparing cops to the average unarmed citizen is kind of apples-and-oranges, don't you think? At least, since guns and things related to guns are the topic of comparison.
To illustrate the point, if I were comparing the driving skills of an average cop to those of an average citizen, a citizen who didn't own a car or have a driver's license probably wouldn't be a good comparison, yes?