The release of the bullet by the neck will play a large part in determining at what point in the muzzle whip the bullet exits the barrel. The point at which the bullet exits the barrel will play a large part in determining where the bullet hits the paper.
Any handloader who has much experience will, at some point (even though it is stated over and over and over in every manual and by every tutor some people just don't get it--at least for a while) have this epiphany: the key to accuracy (defined as having all the bullets land in one place, more or less) is uniformity. Uniformity means that all things are all the same. This means that a .012" neck wall does not release the bullet in the same way or time that a .009" neck wall releases the bullet, so we turn to the same neck wall thickness if we want a certain accuracy. Bullets of different styles and weights fly differently; different powders push differently; and on and on.
The observable effects of component variables in a given rifle/shooter combo will have much to do with the excellence of both and the application. For example, changing the primer to a different brand may not have any observable effect in a moose howitzer like a .300 win mag. but it can ruin a BR shooter's day.
I would bet that for the groups to be so different at (100 yards?) in that kind of rifle, there was a definite difference in the pressure felt when sizing the necks of the two kinds of cases. A clue Watson!
!!!!!
BTW, it seems to me that if all the bullets fired from the brass/brass were in a nice little group and all the bullets fired from the brass/nickle were in a nice group, but just off to one side, it speaks well for the rifle/shooter/lhandoader combination.
OFF ON A TANGENT:
When I was young and in my prime I used to....not feel things like that because I was not thinking about them and I was often in a hurry to load some rounds for--whatever reason. Then I became more mature, attuned to the vagaries of the press and all that and could "feel" even such a small thing as consistency in primer seating with a hand seater. Yahrite. It was soon proved to me that neither my cronies nor I could really "feel" that primer seating like we thought, when another friend had us try it compared to a K&M seater that actually measures such things. Still, since these days every pull of the handle on my press lights up either shoulder I use, I have become even more sensitive to variations of pressure applied when sizing brass than I was in the past. I don't think that anyone, myself included, can operate like a machine and "feel" minute changes in pressure needed to size any brass, but if you keep yourself aware of any gross changes in the seating force needed, you can find errors and variable before they have a chance to bite you on the butt. I've found a few neck turning errors because the force necessary to push a neck past a bushing or an expander button was something I could feel. I am sure a few smaller errors slipped by me as well. Mostly these errors were form being in a hurry,as a lot of errors are.