"The gun is more accurate than the shooter", is probably true, but not really relevant to the question.
No shooter, olympic level or not, could ever truly maximize the accuracy potential of a gun.
Group dispersion will be an addition of error from two sources assuming environmental variations such as wind, etc, are removed:
1) The mechanical accuracy of the equipment fired from a perfect rest (zero shooter error) all group spread comes from inconsistencies in the gun and ammo.
2) Shooter error... there will always be some, regardless of how good the shooter is. This would be measured independently by having the shooter shoot a laser beam offhand from X yards, and the group size is the error induced by the shooter.... (zero variation in the equipment).
The group size is an addition of #1 and #2. No matter how bad the shooter is, all other factors equal, they will be a little better with a more accurate firearm.
I think what people mean to say with statements like "the gun is more accurate than I am" is that #2 is usually a lot bigger than #1, especially with a pistol fired offhand, and therefore #1 is not much of a factor when evaluating the practical accuracy of handguns. Which is true. But it is always still a factor; just one of many.