I don't know if the 6.5x55 is more inherently accurate than most other cartridges or if it had more to do with the quality of the rifles chambered int he cartridge.

1896 swedish rifles were built to standards far higher than most rifles are today.
The kind of things you find in a m96 are what you find in high end custom rifles made today:
actions that are straight and squared.
barrles that are installed square to the reciever and bolt face
piller bedded action
carefully inletted and fitted stocks
barrels that under go tight QC- the bores were guaged then hand lapped after installation


I also understand that the 7.62x54R cartridge is considered to have really good inherent accuracy, though its reputation isn't quite as well known proably becuase most of the rifles chambered in that cartridge are of marginal quality.