I'm a high power shooter, we use irons and 1 MOA groups are not uncommon.
I shot this setting rapid, (using a sling). This was with my White Oak service rifle.
I didn't measure it but judging by the scoring rings on the 600 yard target reduced to 100 yards, its a hair under 1 inch.
What it takes is practice. Natural Point of Aim, Good stock weld keeping your head straight, relaxed position. Looking at the front sight, and most of all TRIGGER CONTROL.
Want to learn to shoot the AR with irons go to the CMP book store and get the AMU's "Service Rifle Guilde" $6.95.