I'm not fully up on the details of the genetic issues, but as an
archaeologist I think it is worth bearing in mind that the ancestors of the present-day
Native Americans migrated into North America about 20,000 years ago,
according to the best current reading of the evidence, and, although there has
doubtless been a certain about of genetic input since then (occasional boatloads of
Japanese fishermen who may have reached as far as Peru around 5,000 years
ago, for example), these have been relatively minor. There are some
interesting books on the genetic evidence for early human migration which is now coming
out. When I started in the field it was thought that the migration was no
earlier than 10,000 years ago, and some still hold to this, but others are now
arguing for a date as long ago as 40,000 years. So a common ancestor with
someone in Japan/Okinawa/Korea would have to be a very long way back.
Rupert