OK, I was being a little naughty.

With open sights/aperture it is extremely likely that a gun will shoot as near POI for the vast majority of different people as to make no difference at hunting ranges.
Yes as has been pointed out above, hold will make a difference to some extent as will gross differences in eyesight.

Scopes can be more problematic for some. Scopes effectively have a short sighting plane. ie the distance between the rear lens and the reticule. This magnifies errors in. Head position, eyesight, and hold. It is a bit like trying to shoot tiny groups with a handgun like the ones it can shoot from a machine rest. It is not a problem with the accuracy of a fine revolver but the short sighting plane. Where you eyes occular centre is can make a heap of difference as can astigmatism etc.

Also there is a bit of psychology involved. If you never shot your rifle on paper and every time you took a shot at an animal it fell over you would never question if it was shooting 2 or 3 inches off. That was exactly what people did. Now we are much more critical about our shooting but hunt less. It is like shotguns, how many people ever pattern them or have one fitted. Most people are happy with theirs, it goes bang and things drop out of the sky. I bet a fiver that 90% don't shoot to POA for their owners.

The difference you experienced in Africa is I believe at the extreme end of what can be anticipated so gives lie to my theory. In that case I think it is hold and recoil reaction/barrel lift. That the 375 had twice the error of a 25-06 is I believe the clue here.

Regards