Non veni pacem mittere, sed gladium.
Hot shot/cold bore, skill of the shooter, cartridge (balanced load, special bullets, etc) all make a 7.62x56 NATO round reach the limit of effective use at the 1000 meter point. Even breeze between target and point of firing creates difficulties for that round (and all rounds) at that range. It will hit at that range - Nossler bullet (partitioned) will help retain mass for killing at that range, but the ability of a sniper/shooter to ten-ring a 1000 meter shot is challenging.
If he's hunting at that range, is there enough velocity remaining to humanely take down his prey? He should've just gone with the .338 to begin with. To be sure.