This sounds like most service pistols are capable of the accuracy needed.
Out to 15-20 yards, this is true of most pistols. It's not terribly uncommon to find pistols that are capable of head shot accuracy out to 50 yards and beyond. However, the accuracy of a pistol, is very rarely the long pole in the tent, so to speak. That's true even at the range, when conditions are ideal.
The fact that I have a pistol that is capable of making head shots at 50 yards, is absolutely no evidence at all that I will able to make a head shot at 3 yards in a gunfight using that pistol.