The Mongols had better accuracy at 420 meters than Olympians do at 70? I doubt that.
Even firing an arrow such a distance was considered a remarkable feat, and it is doubtful that it was ever done with any consistency with arrows heavy enough to have military effectiveness.
Military archery beyond 100 meters at most was always an "area effect" weapon. Massed archers fired at a massed enemy. At such ranges there was no attempt to hit an individual target. Also no need to try.
There are lots of “Mike Fink” tales of amazing feats in ancient civilizations, such as Greek Olympians long jumping 35 feet, etc. Such stories need to be taken with a very large grain of salt.