Yes, it's all about headspace.
I agree with what
@thestelster said.
Let me add that I think you are specifically talking about the Savage Barrel Nut but mixing in information you have heard about shouldered barrel designs (Remington, Winchester, etc). They are NOT the same. But the end result is.
With the savage, it's definitely not a one shot thing. But even the others are not one shot efforts. It's easy to test fit till you get it right.
A yahoo with a pipe wrench is a whole nuther matter.
The part between the barrel and receiver is called a recoil lug. It is not a shim. It transfers recoil forces from the barrelled action to the stock.
They do sell recoil lugs in different thicknesses that can be used to change the head spacing but that isn't generally the way to do it. Normally, the chamber is cut to the correct headspace when it is reamed. Sometimes with prechambered barrels, you can also cut the barrel shoulder a bit to accomplish the same thing with minimum machining. But again, this is not the preferred approach it's only done to facilitate using pre-fit barrels.
This might be one of those things best explained on the phone or hands on during a visit. A visit like that would make it all obvious.