It's not about "accurate" so much. Anything, ANYTHING made on this planet is subject to a tolerance. It's a word that gets thrown around a lot on forums. The thing to remember is that the person designing the part defines exactly what that is.
Example:
If I'm building pallets for shipping boxes of potato chips I may define the tolerance for the board length at "plus or minus" one quarter inch.
(+/- .250")
Another company might say that's silly and open it up to +/- .500". The thing to take into consideration (a topic often overlooked by engineers as they want something they designed perceived as good and they often invest very little consideration to cost) is that adding zeros right of the decimal in a tolerance block always adds zero(s) left of the decimal on the invoice. It's a whole lot less work to maintain +/- .001" than it is .0001".
This "thing" where people say, "my action, gunsmith, (whatever) holds tighter tolerances."
Tighter than what(?) is the first question that pops into my head. It's become a feel-good buzz word that is supposed to conjure up images of someone knowing what they are talking about. Anyone who does this for a living has faced this at least once and truthfully all it does is turn a great hobby into a reality TV show.
Back to the headspace gauge:
You have three basic types. Go, No/Go, and field. GO simply means its long enough for the standard OEM cartridge to fit with an acceptable clearance that mitigates excessive case web growth. No/Go means that same cartridge now fits as a hot dog in a hallway does. The chamber is excessive in length and will promote accelerated expiration dates on brass if it is reused/shot more than a few times.
Field is basically deep enough to take just about anything while ensuring the firing pin will still deliver enough "whack" to make the thing go bang. Nothing wrong with that when the ammunition is a fire and forget type scenario. In some cases where the function is of primary importance, this can be more desirable. -combat being the primary example.
SAAMI, the Sporting Arms/Ammunition Manufacturing Institute is not a law enforcement agency. They provide imperical data that we all base things on, but brand X can do whatever it wants without punity.
In the case of the 308 Winchester SAAMI defines the case head to shoulder gauge line distance at 1.634" as the maximum length. with a tolerance of "-.007".
So here you go: Brand X gauge is on the minimum side of things where's Y was made to the big end. Your gun gets setup with X and the gauge you bought is made by Y. See where this goes now??? All that happens now is the gunsmith's phone starts ringing and he's on trial to explain himself.
Nobody is wrong here. This headspace thing gets so blown out of proportion at times because its "regurgistated" information that some folks don't really understand. If "tighter tolerance" truly means better performance then I would ask why it is that I have fixed more than one rifle in my lifetime that shot poorly just by
increasing the headspace on the chamber.
-that is no shit.
Hope this helps.
Threading is another topic here. Class 1,2,3, whatever... So long as the manufacturer of the action is using a qualified gauge of good quality (hard chromed, ground pitch geometry being ideal as the gauge will be both durable and accurate) and the person threading the barrel blank uses ring gauge of the same size/pitch/class, then there is absolutely no reason to think the thing should not screw together.
Every nut and bolt used to hold anything together on this planet is made this way.
The issue becomes when people think they are improving something. I was a victim of this thought train for a long time. Threads had to be silky smooth or the gun was junk. That has been proven false to me an endless number of times. I know for an absolute fact that my stuff is gauged to size. 99.9% of action manufacturers do the same. The result here is I don't have barrels welding themselves to receivers and suppressors anymore.
Yet, poke around on the web and you'll find someone who is having a mental breakdown because their barrel doesn't feel like a micrometer thimble when they install it onto their action. As a smith, if you try to argue the point you suddenly find yourself as an outcast and you'll very likely have all kinds of free time to manage.
Perspective:
Man built a device that shot another person towards a different celestial body back in the 1960's. That vehicle had less computing power than a 1984 Ford Taurus. (part of my childhood was spent at the Cape, I've been on all the tours

) There's not a single feature on that rocket that didn't experience a dimensional change greater than any single part on a rifle. . .