1stmar, a chambered round's back end is pressed against the chamber wall by the extractor. If the back end of the case is .002" smaller than the chamber diameter at that point, the back end will be .001" off center. External claw extractors push the case head to one side, sliding extractors in the bolt face (push feed Win. 70's] push the case head up.
If the bolt has an in-line spring-loaded ejector in the bolt face, that pushes bottleneck cases headspacing on their shoulder full forward until its shoulder stops against the chamber shoulder. And that very well centers the case shoulder in the chamber shoulder.
When the firing pin falls, that further drives the case shoulder hard into the chamber shoulder. The shoulder's typically set back a thousandth or more from the force of the firing pin's impact. The case is perfectly centered at its shoulder when the round fires. Doesn't matter how much clearance there is around the case body behind the shoulder; it's perfectly centered.
If a case is .001", or even .002" inch off center at its back end, that'll put the bullet's tip in a round with zero bullet runout about half to three-fourths that much off center in the bore. But every round chambered will have the same error; every round's repeatable in how it's chambered. Every rifle made does this; benchrest, match rifle, or sporting rifle with a standard SAAMI spec chamber. There's no such thing as a perfectly centered back end of a bottleneck case in its chamber; external force from the extractor pushes it off center. Doesn't your bolt's extractor hold a case in place on the bolt face if it's out of the receiver?
The .308 Win. and .243 Win. case necks in that .338 Win. Mag. chamber will center perfectly in it as the shoulder angles are equal. There'll be full contact around the case shoulder to the chamber shoulder. The back end of the cases will center in the chamber. Although both cases will have a lot of clearance around them, they are perfectly centered, just like the paper cups are relative to each other.