I guess it's time to dust off the old parallax horse and take it out for another ride.
If you've ever looked through a scope at the target, and noticed that moving your eye around, up/down, left/right behind the eyepiece results in a corresponding shift of the crosshair across the target image; then you've experienced parallax. It is a optical illusion, characteristic of essentially all riflescopes, and it has a relationship with distance.
Unfortunately, unless your eye/cheek weld is perfectly identical for each shot, the POI will shift with each shift of the crosshair across the target image. In essence, even though the sight picture looks identical for each shot, the true POA shifts as the crosshair shifts.
Parallax can be corrected to disappear at a given distance, and many scopes allow adjustment to correct that distance to correspond with the target distance.
Most of those that do will couple this correction mechanism adjustment with the focusing adjustment, even though, technically, they are two entirely different characteristics. Unfortunately, many scope leave the factory with the adjustments not quite sync'd properly. This can be hard to detect, and is probably the most likely cause for undiagnosed issues surrounding dispersion.
If your riflescope is perfectly focused, yet the crosshair moves with the head bob/weave, your scope's parallax adjuster is out of sync with the focusing mechanism. Don't be surprised if yours is. It costs the factory more to get this perfect, and their specs are relatively relaxed in this area unless you're buying a high end optic; this is one of the reasons why high end optics cost as much as they do.
Some riflescopes, usually hunting scopes, do not offer parallax adjustment and arbitrarily set the correction for a distance of right about 200yd.
So how does this affect diminishing/increasing dispersion? A lot, especially if your parallax is set at 200yd, for instance, and you're comparing groups from 100yd and 200yd. Groups at 100 can be larger, measured in MOA, the those at 200. But the reason they are different is because of POA error related to parallax at 100 which will not be present at 200.
Generally these scopes will shoot their best group sizes at the arbitrary correction distance, with group sizes increasing at distances longer and shorter than that distance.
These group size differences are very real, yet they have nothing to do with ballistics.
Greg