By way of example, Schuetzen competition is done largely with 19th and 20th century single shot, 2 piece stock, rifles, at 200 yards on a target with a 1 ½ inch "25 ring", with plain based, cast bullets, either bench rested or offhand.
Before dismissing what is possible, take a look at some of the scores those guys post. In the early 20th century, H. Pope and Dr. Hudson shot some scores that would amaze most of us here.
That said, a well sorted benchrest, bolt action, rifle will still shoot tighter groups today with a good shooter behind it.