Several years ago I owned a pre-war "Standard Modell" in 7X57. I wanted to make myself a 338-06 on it, but never did.
It had a good barrel in it and I used that barrel to build a custom rifle for my brother in law. His rifle shoots so well you'd think I was lying if I told you what he and i have done with it.
Anyway, several years later I took that old Mauser and put a new barrel in it. the barrel was made by McGowen in Montana. I copied the original contours so it would drop into the stock. I took an awful long way around to come back to where I started. I did not use the original sights, but I installed a Lyman 17A front globe sight and a Williams "Foolproof" rear sigh on the receiver. Using my best handloads that rifle would shoot under an inch at 100. I did it many times and so did several friends of mine so it was not just a fluke.
I think this story may be relevant only because the original barrel was at least as accurate as the one I replaced it with. I know because I made a good deer rifle for my Brother in law and zeroed the rifle for him with my loads before I am my wife gave it to him for his birthday. It went to him with a Leupold 3X-9X scope. I was actually shocked to see how well it shot .
Later when I returned the Standard Modell to near military condition the only thing that was not in "issued condition" when I did shoot those sub MOA targets with that rifle were the sights and the new barrel. I am sure I could have done the same thing with its original barrel now, but I didn’t think that when I took it out of the action. I should have tried it first I guess………..
So I know it's not common, but a good Mauser in military condition can be sub MOA accurate now and then. Most would shoot about 2” with good ammo when they were brand new, but every now and then you may get one that will shoot under 1 MOA.