The Marine qualification with the M16 runs out to 500yds, but I think the course requires only five rounds at that range for the old qualification and if you have shot well at the shorter distances, the 500yd shots don't really matter and you are not expected to get many hits at that range. I am not totally sure, but I think a hit is about 3MOA at 500yds.
I don't expect ex military friends of mine (I never served) to always be exceptional marksmen, and they usually aren't. They tend to be better with a rifle than a pistol too but that is generally true for everybody I guess.

I think that stems from that in the battlefield, a hit is often better than an outright kill.
And that speaks to the question at hand regarding the 308.
The USMC website suggests that in the SASS, it can "deliver precision fire to enemy targets to 800yds". Not sure if the enemy target is a single man or vehicle, etc., but if it is a man, that is about 2MOA or a bit more at 800yds for a torso hit which is close in size to the vitals of an elk. Add to that, that the USMC is looking for hits and a hunter is looking for a clean kill (or should be).
As mentioned above, the question about retained energy and velocity to get adequate bullet performance becomes the most critical point in whether the 308 is a capable long range hunting proposition and IMO, it is not even at 500yds. Long range plinker, yes, long range hunter, nope.