Sorry that statistic seems completely impossible -- how would a man alive just before the roman republic became an ancestor to the Gauls (whom the Romans wouldn't discover for quite some time) let alone the American Indians?
All people alive today, not all people ever. The article cited[1] quotes indigenous populations in North and South America dropping by 97% and 93% before 1570— in the centuries since, it has become statistically improbable that any Native Americans descendants exist who don't share a European ancestor with you.
Now it comes from a computer model, so there could be errors or exceptions— I'm thinking extant uncontacted peoples, here. The model accounted for this possibility, as the paper notes: ...in order for a remote island to affect the MRCA
date, it must have been colonized prior to the lineage of
the mainland MRCA reaching the source population and
it must have remained genetically isolated until very re-
cently in order for there to be surviving people with no
modern mainland ancestry.
Remember that uncontacted peoples are uncontacted by us; the ones we know of have regular if infrequent contact with other tribes, so if contacted tribes share the MRCA it's quite probable that uncontacted ones do as well. Could there be a cache of 50-100 human beings somewhere on this planet who happen to share an MRCA with us who is older than the one shared by all other living persons, maybe 10,000 years? Sure. But they would be the only ones out of 7 billion.
They probably wouldn't no. However he's talking about humans alive today. Whilst I'm not really keen on this distant ancestral concept due to it essentially being a statistical trick, it's not unreasonable to assume that the descendants of Gauls/etc would have married someone in that descendancy tree, somewhere along the way.
The place this really falls down would probably be extremely isolated tribes which have had little if any external contact - there's very few nowadays, but some are remote enough that no pairing has probably happened.
