Oh dear. The dreaded runout issue.
Years ago the guy who made NECO runout gages did some experimenting and determined that the brass which forms cartridge cases is not of uniform thickness all the way around the case. This lack of uniformity would cause the cases to perform differently when under the pressure of being fired. They would bend towards the thickest part of the case causing a "banana" shaped case, which would tilt the bullet in that direction as well.
IIRC, he had a device or tool which would assist folks by determining where the thickest part of the case was, so they could index the cases in their rifles causing the bullet tilt to be more consistent. As Unclenick so eruditely explained, if the bullets are all tilted in the same direction, they will group accordingly.
So, while I haven't followed up on this any further, whether the necks are straight or not, whether sized in a bushing die or FL die or not, one will achieve greater accuracy indexing his cases in his chamber towards the thicker side of the case. Perhaps file a notch in the case rim at the thick part, and orient the case towards 12 o'clock or something.
It makes sense to me that if, prior to firing, all the bullets are relatively straight in the unfired, loaded cases, then the inevitable tilt towards the thick side of the cartridge upon firing will also be more uniform. Ferinstance, if bullets have random runout all around the clock face from the thick side of the case, they may exhibit more random groupings on the target than if they were "straight" prior to firing.