even with a rifle, in a stable position, shooting a moving target is extremely hard while popular culture makes it look trivial.
Over here moose hunting is quite popular; to keep their moose hunting license every hunter needs to pass a test (every year, IIRC) that involves hitting a moving target.
Most hunters pass this test without much difficulty. Of course, on the range the distance is known (100m, IIRC), and the target moves at a constant and known speed, so one knows how much lead is needed. Still, AFAIU in the wild the results are decent.
On the other extreme, top Steel Challenge competitors can consistently shoot 5 different targets in 2 seconds, starting with hands above shoulders.
Most of those officers can do pretty well on the range, too. Problem is, adrenaline plays hell with fine motor skills - there are even specific techniques for reloading that I've been taught that require only gross motor skills, because that's all you'll have in an emergency situation.
Having spent a fair amount of time in my youth shooting with a BB pistol in my parents garage, I find the above statistic entirely believable. Shooting a pistol accurately is much more difficult than it looks, so I can certainly imagine that in a high stress situation where your own life may be on the line you'll make simple mistakes that cause you to miss..