I have heard this often enough that I can't really dispute it and it makes a certain amount of sense. I just have not verified it with a controlled test. I have had experiences with cases which are supposed to be "stretchers" and found them to be not so bad so I question the reason for the stretching.
For instance, the 303 British case stretches; not because it has lots of taper and a shallow shoulder angle but because the rifles it is most commonly chambered in are stretchy. The 270 Winchester is purported to stretch pretty badly but mine does not.
One fellow came into the shop with a 6MM Remington which stretched cases badly. It turned out the boltface was badly off from perpendicular (about .004"!) and the brass was stretching to fit the bolt. Each time it was fired it had to do this and the brass ended up stretching rapidly.
I suspect the more precise headspacing afforded by the sharper shoulder may well have more to do with any reduction in stretching than anything else does. After all, it makes little sense that the rounded corners of the Weatherby shoulder would inhibit brass flow. It does make sense that the case is more positively headspaced.
If one was to test a standard 30/06, for instance, and keep track of the amount of stretching; then rechamber the same rifle to 30/06 AI and repeat the test; the results would have some validity. One would have to be sure and just partially size the cases to insure the shoulders were not touched and load similar loads in each. I've got a bunch of old 06 barrels just taking up space. Maybe I'll try it sometime. The rimmed 303 or 30/40 could be used to test the precise headspacing theory. If closely fitted, the rim would take the shoulder angle out of the equation as far as precise headspacing was concerned. I'm too busy now but maybe this summer sometime.GD
