According to the NRA Handloading book, a .308 chamber is 1.630" min., 1.640" max.
Ammunition for .308 is 1.634" +.000", -.007".
This means it's conceivable you'd have a .004" interference fit.
However, most ammunition I've checked on a Wilson case gage is close to or smaller than 1.631". And yes, I used a headspace gage to check the Wilson.
The problem is Nato chamber spec. runs 1.635" min, 1.6455" max. The "extra" allows for dirt and mung.
I can't find other than anecdotal evidence for the spec. on NATO 7.62x51 ammunition, but have never measured one over 1.633". That doesn't mean they don't exist, just that I've never found one. My samples were many and included West German, Israeli, Portuguese, Australian, South African and a few from Venezuela.
Of rifles I've seen, the only one that ever failed with commercial .308 was a Century Cetme. Cartridge separation with the first shot of Remington hunting ammunition. It worked fine with Portuguese and South African surplus. The rifle swallowed my .308 Field Gage.
The anecdotal upshot is if you have a longish chamber relative to .308 in your military type rifle, use NATO surplus. My M1A headspaces at 1.632" and has never failed to feed and shoot ANY .308 or 7.62x51 round.
