Someone (Mike Venturino?) did an article on military 30-06 ammo in a Handloader a couple years ago. He found that in THIS CALIBER, military brass and commercial brass have virtually no difference. Certainly no more than the variation that one would expect between different manufacturers or production lots. The caveat about mil. brass being thicker is much more correct for 223 vs. 5.56 and 308 vs. 7.62.
Sir, when I was shooting NRA high power (up to a few years ago) I weighed a lot of brass, and my experience differs from the article you cite.
All the R-P and Winchester commercial .30-'06 brass I weighed were invariably much lighter than LC, TW, and SL .30 M2 brass. Federal commercial .30-'06 brass did weigh essentially the same as USGI .30 M2. Unless the manual you're using specifies Federal brass (as Sierra Edition V does) or GI brass, it's wise to drop down 2 grains from the manual's recommended powder charges.
All the USGI 5.56 brass I checked (LC mostly) weighed essentially the same as Winchester and Federal commercial brass. Still wise to check brass weights and to work up loads carefully, but at the end of the process, the loads will probably end up pretty much the same.
The only commercial .308 brass I weighed was Federal, and it (like Federal commercial .30-'06) weighed essentially the same as its GI equivalent. I would not expect this result from other brands of commercial brass, though. When in doubt, check.
So, long story short: The caveat about military brass exists for a reason. It's not true in every single instance, but it's true in more than enough instances to warrant caution. Weigh the brass you're using and compare it to the brass specified in the manual. Don't just take someone else's word for it.
Hope this helps, and Semper Fi.
Ron H.