I don't believe the K31 is any more accurate with ammunition tailored for it than any other milsurp in the same condition.
I have taken pristine condition milsurps to the range and had several different shooters compare them, by shooting tailored ammo for each, off the bench at 100yd targets.
The idea was to compare groups, not shots on center bull. The center bull was used as an aiming point only. It's next to impossible to set the sights on a rifle for every different individual that shoots. it.
There was one fool that kept trying to apply "Kentucky windage" so that the POIs were close to center. He produced nothing but large groups, while everyone else produced groups in the 1 MOA range.
All of the rifles were stock milspec with no modifications to anything, including sights.
The rifles used for this comparison were a M96 swede, M91 Argentine, M93 Spanish, Gew 88, Brazil M1908, BYF Mauser 98, Longbranch No4 MkI*(1950), 1903A3 Springfield, M41 Carcano and a Type II Italian built rifle for Japan during WWII, which looks like the bastard child of a Carcano and Arisaka, M91 Mosin Nagant.
As mentioned, all of them were in pristine condition and that's why they were selected for the comparison. All the shooters, but one, were on the ball, lots of personal knowledge about the types of rifles and all shot those rifles very well.
The ammunition was all hand loaded with Hornady bullets, and once fired brass.
There was only one of each rifle. All were mine. That was the control factor for the comparison shoot.
It was a great day for all of us and in a couple of cases, opened a few eyes to the capabilities of these rifles in as new, unissued condition.