To start with I want to say that Mathsr is my brother and I have a little more information on this topic. He is dealing with custom premium grade barrels from manufacturers you would all recognize. He doesn't want this to be about a barrel maker and is not throwing stones, just trying to get informed. The barrels (2)have been ordered pre turned to a .600 muzzle and came at a 26 or 27 inch length. When cut off to 22 inches the bore was noticeably off. On the other end of the 4 inch section it appeared to be centered. We are talking .020 inch out in 4 inches. I don't know what it was out at the middle of the barrel.
This has also happened with several barrels that came on a commercial rifle and one of the problems was that the barrel was crowned concentric with the outside diameter of the barrel and not with the bore. When re-crowned with the bore they shot better groups when allowed to remain fairly cool. If you shoot a fast five they walk a couple of inches.
I am thinking it may be more of a problem with light sporters than target or varmint weight barrels, with .020 being a higher percentage of barrel mass on a sporter weight than on a target weight.