Provided the brass isn't too long, I would bet the shoulder is what is contacting, not the bullet. Hard brass explains the difficulty in resizing.
IF the privi ammo was cheap..... Well there you go.
Also IF it was manufactured to 7.62 NATO specs that can explain the shoulder issue. It is a popular belief that the NATO and 308 chamber are the same, however. If you look at the NATO drawings and field gauges, the NATO chamber can swallow the 308.
Meaning if you have a tighter-end 308 chamber, and the ammo is larger NATO spec, you have an interference fit.
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