You can chamber a .308 in a 7.65, which is why I asked. I suspect he is using the wrong ammo and blowing the shoulder too far forward to be resized. If the original barrel has been set back and rechambered, he would need to use the larger bullets as you note. That may be what has saved him so far if he has been using the wrong ammo. The undersized bullet would reduce pressure. If it has been rebarreled, it may indeed be chambered for .308 Win and have a .308 groove diameter.
The whole idea scares me. The '91 action is not strong enough, nor does it have the capacity to handle escaped gas to be shooting .308 Win in one. Further confusing matters is the Spanish 7.62 CETME round which is dimensionally identical to 7.62 NATO, but loaded to much lower pressures.