I've had one Rem in my life that shot 1moa right out of the gate brand spanking new. If memory serves it was right at .850 on a 5 shot run. Had a few Win's that were superior rifles right out of the box from the the very early 60's. Even have 1 Marlin lever gun 30-30 that will hold just a tick under 1moa as long as I take my time after the first 2 shots. She strings a good bit heating up fairly quick. But I also know that rifle well enough to compensate pretty darn well for it's vertical string and adjusting my aim.
As far as AR's go, there are SOOOOOOOO many companies out there now slapping parts together it is dang near funny. But there are a few you can go to to have one built that will fix you up with a dang NICE shooting rig. My 6.8SPC will easily hold between .550-.750 as long as I aint trying to speed demon the trigger. Now my .458 SOCOM while it isn't a serious tack driving machine, it will hold between 1.0-1.5 which all in all is pretty dang sporty for what it is. Then we come to my little gem 7mm-08 AR10 that will consistently print one small ragged hole at 100 yards again as long as I don't try breaking any speed records on trigger time. Now my new .338fed AR that NoMercy helped me acquire I haven't had the chance really to put through any serious loading and testing so far but what little I have fired it, it seems to be a pretty dang good rifle. Another one ragged holer.
Now, like RR, I haven't bought more than 2 or 3 boxes of factory ammo in 45+ years for rifles. I learned WAY early on that factory ammo has the consistency of a 3 year old little boy. Everywhere you DON'T want it to be is exactly where it will be! So many factory rifles, while they might not shoot worth a tinkers dam with factory ammo, might just jump up and surprise you with some tender loving at the reloading bench! You also need to learn the "personality" of your rifles.