RE: shot out barrel
The worst shot out barrels aren't going to shoot that bad. There are other issues going on here- bad crown, loose action screws, loose scope mount, poorly bedded stock (yes, not all gunsmiths are competent), even the free floated barrel could be the cause if the rifle likes upward pressure at the front of the stock, and last but not least, the shooter.
As far as shot out goes, I have a 60 year old turk mauser that actually has some of the lands worn out of the barrel that will shoot 5 inch groups at 100 yards- with crappy surplus ammo.