From what I've seen it relates to the height of the sights, almost the same way that mounting a scope high over the bore of a cartridge rifle really affects your mid range impacts. Don't know if that makes sense, but all the guns in our group with longer barrels tend to have very low sights, while the shorter ones tend to have taller sights along with their shorter sighting radius.
Remember that for a 50-yard POI, the bullet starts out below and arcs up to line of sight, and may actually pass over it slightly before dropping back down to your point of aim. The higher the sights, the lower it's going to be hitting early on in its flight.
I feel like I'm talking in circles (and maybe I am), but the point is that there's no free lunch. Even if gravity weren't at work and a bullet traveled absolutely flat, it still starts below the sights and catches up with line of sight at your point of aim. Since gravity works, it actually starts falling the moment it comes out your bore, so it's doing an arc rather than traveling in a straight line to hit point of aim.
Changes in velocity (and time of flight) resulting from changes in powder charge or barrel length also affect the shape of the arc.
Long and short of it, for the guns our group has been shooting, short barrels result in more change of POI close to the gun than is true with longer barrels, whatever the cause and however good (or bad) the explanation.
If you are a small game hunter aiming at close-range small heads, it's simply a matter of shooting it at closer ranges as well as at longer ranges when sighting in. As I said before, being an inch off on deer lungs at 50 yards isn't as big a deal to me as being an inch off on a squirrel or rabbit head at ten yards.