Besides a out of round chamber the same thing can happen if the cases have unequal case wall thickness. When these cases are fired the thin side expands more and causes the case to warp. The base of the case will not be 90 degrees to the axis of the bore and the case ends up banana shaped.
In some of my milsurp rifles if the case was placed on its base you could actually see the case leaning.
NECO CONCENTRICITY, WALL THICKNESS AND RUNOUT GAUGE
Also referred to as "The Case Gauge," this item is designed to measure:
1) The curved "banana" shape of the cartridge case;
2) The relative wall thickness variation of a cartridge case;
3) The cartridge case head out-of-squareness;
4) Individual Bullets - out-of-round "egg shape" and/or
curved "banana" shape (excepting very small bullets);
5) The seated bullet and cartridge runout of loaded rounds.
http://www.neconos.com/details.htm
Below is from the now closed website "The rifleman's Journal" and the subject was partial full length resizing. My main point here is the case is supported by bolt face in the rear and by the bullet in the throat. And with a full length resized case the case shoulder is the only part of the case that "should" touch the chamber walls.
Reloading: Partial Neck Sizing
by German A. Salazar
http://riflemansjournal.blogspot.com/2010/06/reloading-partial-neck-sizing.html
"Now the last scenario, a full-length sized case in which the neck is also fully sized. There is clearance at the neck and in the body of the case, the closest fit anywhere is the bullet in the throat. If the neck to bullet concentricity is good (although it needn't be perfect), then the bullet will find good alignment in the throat and the case body and neck will have minimal influence. Let's not forget that the base of the case is supported by the bolt face or the extractor to a certain degree as well; this is yet another influence on alignment. As you can see, there are several points from base to bullet that can have an effect. My procedure is to minimize the influence of those that I can control, namely the case body and neck, and let the alignment be dictated by the fit of the bullet in the throat and to some extent by the bolt's support of the base. Barring a seriously out of square case head,
I don't think the bolt can have a negative effect on alignment, only a slightly positive effect from minimizing "case droop" in the chamber. Given that a resized case will usually have a maximum of 0.001" diametrical clearance at the web, this isn't much of a factor anyway."
The newer model 70 have a completely recessed bolt face and should not have excessive case droop. Meaning the rear of the case should be kept fairly well centered by the bolt face.
Below a pre-64 bolt face on the left and a post-64 bolt face on the right. And the newer bolt face should not let the case move or droop excessively.
If you want to talk about case droop then buy a British.303 Enfield rifle where the bolt face does not support the rear of the case. And the cartridge just lays in the bottom of the chamber.
In another article Mr. Salazar had a similar problem like yours and it turned out to be defective cases. I have had Remington cases with over .009 case wall thickness variations and they warped and were a pain in the back side until I found the problem.