You can have a yard of perfect rifling from the breech to the muzzle, but it only takes a couple of tenths of a millimeter of asymmetry at the muzzle to send the shots off course. If you can see it, don't assume it's trivial. A light touch with a crowing tool to restore the best possible symmetry will be invisible after a few sessions at the range have dulled the shiny new surface, and it may well cure the off-axis grouping.
The wear on the school gun may be symmetrical, and therefore have little effect.