I have observed this with the M-1, M-14, AR-15 (SR-1) and FAL, which is why I stopped using semi-autos in competition when the LIEberals brought in the mag restrictions on semi-auto rifles.
Problem is that the rifle/ammo/shooter combination usually is not good enough to show this phenomenon, but it is there and it does show up if you use enough sandbags and if your ammo is precise enough. Generally, it does not show very clearly with factory ammo, although some lots ARE consistent enough to show it.
I think it's to do with charge positioning/compacting in the case, or with primer pre-pressurisation, both results of the 'enthusiastic' operation of the rifle mechanism.
With my M-1, the first round is always outside the Men Point of Impact.... and so is Number 8. So you get a 6-round tight group with 2 flyers, 1 low and left, 1 high and right. FAL does the same thing except that you now have 1 low and left, THREE in your group, 1 high and right. You USED to be able to shoot a 12-round target with the FAL (2 sighters + 10 to score) or even a 17-round target (2 sighters + 15 to score) but the mag restrictions have scrood this completely because you no longer have enough sighters for the rules. So I stuck with bolt rifles until my heart started doing funny things. Now, I just pray a lot and, once in a while, hit something..... if it's big enough.
Prior to the mag restrictions, my practice was to waste the first round as a warmer.... but it did give you a pretty good idea where your group was going to be. I pretty much gave up on it when the mag restrictions came in because it was taking 8 rounds just to put 5 onto the paper.
But, of course, we all know that target shooters can get exemptions from the mag restrictions by applying and the Gummint would NEVER restrict a legitimate SPORTING use of firearms. Mister Trudeau PROMISED that. So did Mister Cretin. So did Prime Mistress Campbell and the others.
Liars, damned liars, lawyers and GOVERNMENT: in that order......
The difference between your Enemies and your Government is that your Enemies are honest enough to TELL you that they are out to destroy you.