If you take a case headspace gauge to new ammunition you will find the cases are typically under minimum chamber headspace length. I find 1.628" pretty common in new commercial brass. The manufacturers know what they are up against, and despite the fact the SAAMI specs allow some overlap between maximum case and minimum chamber, I've never seen a case that even approached maximum. Indeed, even the surplus 7.62 I've had has never exceeded minimum chamber length, though it wouldn't surprise me if it happened somewhere.
Hatcher mentions that he'd measured .30-06 cases that shortened as much as 0.006" just from vigorous chambering in a 1917 Enfield, so this is nothing new or special. Closing the bolt on a long shoulder just displaces the brass into the extra width available for it in the chamber. If you need a hammer to close a bolt, then you have more interference than the extra chamber width can accommodate, so SAAMI specs are likely being exceeded in one place or another. SAAMI specs are all about compatibility.
Bill,
I'm not sure what the Gunsmith in the video meant. Perhaps he was referring to how much the chamber stretched when you tightened the nut? There is no special Savage-sized GO gauge any more than there is special Savage size .308 Wichester ammunition. The gauges, if made properly, are a single standard from the breech face to the 0.400" diameter at the shoulder, which is called the shoulder datum. Below are the case and chamber headspace specifications. The object is for the cartridge to fit in the chamber, even if that takes a little expanding, and all are alike in that regard.
I will say that I have some cheaper gauges that were off by as much as 0.002". Maybe that's what the AGI gunsmith was worried about. Dave Manson, Clymer, JGS, and Pacific are all good brands, and if you have one of their gauges the length isn't likely to be off.
One thing to understand is that the GO and NO GO gauges are for a newly installed barrel. The reason the FIELD gauge is longer is to allow for bolt lug setback over time and for barrel thread burrs and surface finish all to settle out with some shooting. So your gauge and tape may fit after awhile and you could still be in spec, though you could also choose to get out the gauge and set it back again for longer case life.