Did you/they use a pre-20th century bow and arrow?
Recurved bows of composite construction were used well before the birth of Christ. Also, many of these archery feats have been replicated with simple longbows. You saying that it is unusual or especially difficult to achieve accuracy with a bow and arrow simply isn't so...although I guess it depends on how you define "accuracy". Man sized target at 200 yards though? Very doable by a good archer. Many people hunt big and small game successfully with bow and arrow, and like I say, a few can even do things like bring down flushing pheasant reliably enough to not be a fluke. And many of these people use the "instinctive" shooting method, to say nothing of shotgunners who commonly use a similar method for wingshooting.
Bringing things back to topic, IN *any* kind of close-range shooting of a moving target with significant angular problems to solve, a sight is merely a reference point whose value may be quite limited.