My model 760 .30-06 shot right at MOA with premium ammo, but I had to switch to managed-recoil (doctor's order) to keep shoting it. Now it shoots 1/2 over MOA if I hold up my end of the deal. That's OK with me since I'll rareley get a shot over 100 where I hunt. I have a Saiga .223 that shot 3" with silver bear ammo and shoots 1.5" - 2" with core-locts. It did shoot one group with all the holes touching, but I know it was just luck.
My favorite target shooter is my .22. It is an old Romanian training rifle I got for $40. Really cheap fun.
This is a 40-shot group at 50 yards, open sights: