The votes for the 222 as an inherently accurate cartridge stem from it's use as the predominant BR cartridge through the 1960's and early 'seventies. While the 222 is no longer available in the "econo" rifles, having been supplanted by the 223, it was commonly available in these sorts of rifles back in the day.
The only way to determine the inherent accuracy of any cartridge is to establish how accurate it is in a rifle built to allow the cartridge to do perform as well as it can. In other words, a given cartridge can't be given a pass just because it is mostly available in inaccurate rifles. Likewise, a cartridge can't be discriminated against because it is most often used in purpose-built rifles. When you are discussing cartridge performance, all else has to be equal. Otherwise you are discussing rifle performance; not cartridge performance.
By the way, I don't think there is much difference between the 222 and 223 in similar rifles. The 223 may have a bit of an edge because the greater capacity allows greater latitude in the choice of components and allows decent velocities at lower pressures if desired. GD