Whelen liked accurate rifles both for their own sake, and because he was a New Endgland woodchuck shooter. But I doubt he was so picky about his big game rifles.
My experience is that any rifle that averages 1-1/2", 3-shot groups at 100 yards will kill big game a lot further than most hunters can. Have used several to take big game neatly out to 300-450 yards on numerous occasions, and the only problems encountered were when I read the wind wrong or had a brain-fart. The accuracy of the rifle was never a problem.
Of course, I'd shot them all at longer ranges, so knew they'd keep their shots within 3" of point of aim out at 400. With typical heart-lung shots all you need to do is hit a volleyball-sized area, and even a pronghorn's chest is larger than a volleyball.
I like accuracy as much as the next guy, but suspect a lot of the obsession with "deer rifles" shooting sub-inch groups is that the average hunter/handloader spends a lot more time shooting off a bench than he does hunting, and counts his loading room and bench time as part of the game.
