Oh dear....
Yes, it is very puzzling but it is theoretically possible for bullets to produce smaller MOA groups at 2-300 yards than at 100. I didn't read all of Bart B's posts carefully, but I think he has it about right.
Someone made the comment that the tip of the bullet traces out circles as the bullet travels. That is correct. Further, the drag vector on the bullet always points directly from nose to center of base. So when the nose points toward 3:00, the drag vector still points mostly backward, but also a little toward 9:00. This will pull the bullet toward 9:00. 180 degrees later, when the bullet nose points to 9:00, the opposite happens and the bullet is pulled in the other direction. That is the source of the "restoring force".
The effect is fairly small. You probably won't detect it with your favorite SKS. But, yes, the bullet does move up, right, down, left, and up again. This effect diminishes as the bullet gets farther from the rifle. The force is a product of fluid dynamics, and would not happen in a vacuum.
Note that wind drift is NOT a product of the wind blowing against the side of the bullet, at least not mostly from that. Wind drift happens because the bullet noses slightly into the wind to keep the drag vector running from nose to center of base. The horizontal component of that drag vector is almost entirely what moves the bullet in the direction the wind is blowing. Bullets with higher BCs have smaller drag vectors, and that is why they are less affected by the wind.