I have had a couple of rifles that would not take a go gage, but would chamber new factory ammo and unfired cases. I left them that way without any problems. On the belted cases, you might need a little more room if you switch ammo or use reloads fired in another rifle. Headspacing on the belt makes them unforgiving if the chamber is even a tiny bit short. I like tight chambers for accuracy and case life, but you have to be sure that the ammo you use will chamber cleanly.
I recommend getting your 'smith to try his go gage again, and if the bolt will close, then add shims until it won't. Then you will know exactly where you are. Presuming that the rifle is not a benchrest gun, if the bolt won't close on the go gage, I would touch the chamber with the reamer until the bolt will just barely close.
This is just my opinion and preference.
Good shooting, Tom
Texas State Rifle Association Life Member
NRA Endowment Life Member
A big fast bullet will beat a little fast bullet every time