First depends on what you mean by accuracy. Is it the best 3 shot group, or on average 5 shot group, or the diameter of the target you know you hit with first shot at 99% probability when you take the gun out of safe and go shoot it?
The Internet is full of guns that shoot 0.3 MOA all day but those are rare on the range and when hunting, precision is more important than accuracy. If you've got a rifle you know reliably hits a 1 MOA target with the first shot you're in good position and improving the rifle's mechanical accuracy is not bringing much benefit in hitting the target at long distances where the majority of the error is caused by the muzzle velocity variance, error in range and wind estimation and other external factors.
Not saying I'd be happy with a 1 MOA 3 shot grouping rifle neither, but instead of trying to achieve super tight groups try to minimize the distance of the worst shot from the aiming point. And remember, a 1 MOA rifle can reliably hit a 8 inch target at 800 yards. That is a lot harder than shooting tight groups. Humane kill at long ranges is more dependent on the location of the group than the group size as long as the rifle is adequately accurate which I'd say anything that reliably has a hit rate of >95% at a 1 MOA target is.