You can get 5 rifles brand new production out of the box and no two will fire alike. They all have a happy load, but they may not be the same.
I beg to differ with you on that statement. I will agree that it is 95% correct though. I have had 10 different Brazilian Mausers chambered in 7x57mm on the range at the same time. 5 model 1908, DWM and 5 model 1935, DWM. All were new in grease when I got them and all came with their full contingent of accessories including their factory group targets.
The ammunition used in this test included 20 rounds each of handloads that duplicated the Brazilian issue loads. The brass was Norma, the primers were Winchester Standard, the powder was W760(similar to the ball powder used by Brazil from 1940 on) and pulled 140 grain SPBT FMJ bullets from a lot of Brazilian surplus that was sold as components only. The brass was fine but the powder and primers were not trustworthy.
Every single one of those rifles, even though their serial numbers were all over the place and from different runs, shot sub moa groups to POI, eight in high at 100yds. They had been properly cleaned as far as the bolts and barrels were concerned. I didn't want to strip them down for fear of buggering up the screws or marking the stocks. That's it. Nothing else done to the rifles.
I bought the rifles through a deal I made with Les Viel of Vernon, now deceased in 1976. He bought a case of 1908s and I bought a case of 1935s. We split each case by taking the top five rifles off the top of each case and putting them in the other. The only thing we were careful of was to make sure they had matching targets and bayonet numbers. No, the cases themselves weren't Brazilian. International put them into crates they had on hand. I don't know how they came in. We expected the serial numbers to be consecutive but they weren't, which leads me to believe they came from different sources, such as police, military and whichever various government employees the Brazilians armed. Considering the last time I was in Brazil, the firemen carried arms that could be just about anyone.
Whatever, it made for a pretty decent test. I sold off most of my rifles over the years. I still have one of each left that are pretty decent and still in VG+ condition inside and out. I have shot several different batches of surplus ammo through them with bullet weights of either 140 SPBT or 175 RN. They shot as consistently as the ammo would allow.
As far as other rifles go, I confess, I pretty much agree with you. Even when there is no measurable difference in the chambers or barrel dimensions will shoot to very different points of impact with identical iron sights and the same factory ammo lot.