falldowngoboom, there's a lot of misinformation in print (in books, magazines and on line forums) regarding what happens when a rimless bottle neck case is fired. Most of it's based on improper or incorrect case measuring for each phase a new case goes through from first firing through reloading then firing again. Here's what happens with a new .30-06 round of ammo.
When loaded, it rests in the chamber until the firing pin strikes it. When the primer's struck with some 25 to 30 pounds of force, that energy drives the case forward against the chamber shoulder. The force is enough to set the shoulder back shortening the head-to-shoulder length a few thousandths. This also pushes case brass into the chamber neck making the neck a bit longer. As the powder burns increasing pressure and expanding the case body against the chamber wall, that stretches the brass pulling the case neck back a bit in the chamber's neck. At the same time, the case body stretches back until the case head's stopped against the bolt face. The resultant case dimensional change is its body is now greater in diameter at the shoulder-body junction as well as the pressure ring which is about 2/10ths inch in front of the case head. More brass moved expanding the case body diameter than changing the neck dimensions so the fired case is now shorter.
When this fired case is full length sized, its body and neck diameters get reduced and the brass has to move someplace, so the case gets longer. The dimensional changes are such that after a new case is fired it gets a few thousandths of an inch shorter, but resizing it makes it a couple thousandths inch longer than when it was new. With minimum full length sizing, the case will be almost 1/1000ths longer after each cycle. The more a fired rimless bottle neck case has its diameters reduced when sized, the more growth in length it has from each fire and resize cycle it goes through. This is what the quote means you mentioned:
"The walls of a case become thinner as it stretches from repeated firings and resizings. As a result, the neck section will thicken because of the forward brass flow."
It mentions "firings and resizings" which is the key phrase.
As most folks using full length sizing dies on such cases work the brass too much by setting the shoulder back too far (more than 2/1000ths) and reducing fired case diameters too much (more than 3/1000ths). And they may well get better accuracy and longer case life with neck only sizing their fired cases. This will cause a lot more brass to flow forward thinning the case at its weakest point; the pressure ring about 2/10ths inch in front of the case head. Folks who full length size .30-06 cases the best way usually get a few dozen reloads per case; sometimes more. Neck thickness doesn't increase any significant amount but case length will grow about 10/thousandths after 10 fire & resize cycles and need to be trimmed back. I've shot and fired a .308 Win. case almost 50 times full length sizing this way with excellent accuracy, low muzzle velocity spread and didn't anneal the neck at all. Others have done the same thing.
Benchresters have used neck sized cases for years but there's more of them full length sizing nowadays. They don't reduce fired case diameters nor set shoulders back more than 1 or 2 thousandths and get exceptional case life. The claim made by neck only afficianados is it centers the bullet better in the barrel. Both neck only and full length sized cases center the neck and bullet perfectly when fired as their shoulder's forced to center in the chamber shoulder when the firing pin drives the case forward. It doesn't matter how much clearance there is between case neck and chamber neck. And both types have the case back end pressed against the chamber by the extractor, so the back of the case isn't ever perfectly centered in the chamber. Every round fired has its long axis a tiny bit misaligned with the chamber axis. Not many folks realize this is what happens.
