Van, I think that there are maily two reasons that the "varmint" rifles generally preform better than the average centerfire hunting guns.
1.Less recoil= more shooting= better groups.
2. Most varmint guns are heavier, bull barreled guns, whereas most hunting guns are lighter, thin barreled guns.
As guns go, I don't think the barrel thickness really makes the barrel more accurate. It is just that the increased weight makes for a more stable platform.
Back to MOA, I think the quality of most newer guns today, is that most, not all of them are capable of tight, consistant groups.
Speaking for myself, just about all of my equipment, is far better than my ability!