You know, I've said this before but I will say it again anyway. Machining does not add stress to the barrel UNLESS the machining is done with a dull tool which displaces metal rather than cutting it. Machining removes material and, with the material, removes any residual stresses. When the stresses are removed, the material moves. When material is properly stress relieved, it is mostly inert. I say "mostly" because the stress relief process may not have been perfect and there may be some residual stress in the blank.
I once had to machine some steering racks with integral hydraulic pistons. For this I ordered some HTSR 4140. The piston was 1 1/4 in diameter while the rack was .750 and about 32 inches long. The teeth were cut about 35% of the way through. I made 3 of them and the first one warped pretty badly. I stress relieved the other two pieces of material by putting them in a piece of 6" tubing and heating it with a tiger torch until my RadioShack heat sensor thingy showed it to be at about 1100 degrees then I covered it all in sand and left it overnight. The pieces machined from this material stayed nearly perfect even when I cut the teeth in the shaft. Obviously the machining was not inducing stress. The stress was there in the first place on the first piece of material and the machining only allowed the stresses to have an effect.
By the way, MRC barrels are properly stress relieved. I've seen their furnace and seen it in action. I've also turned their barrels with minimal movement.
Barrel makers usually use material which is stress relieved prior to working on it. Some will have it relieved again after drilling. Those makers who produce button rifled barrels must stress relieve after buttoning since buttoning does introduce stress into the barrel. This is because it is a swaging or metal displacing procedure. Those barrels which are cut rifled don't generally require stress relieving after rifleing. That is, they don't if the material was properly stress relieved to start with.
Cryogenic treatment is not true "stress relieving". It may have some effect but seems primarily geared toward improving machinability and surface finish. Regards, Bill