I don't rule out the possibility that some Halo-X may also have arrived from across the Atlantic.
That's pretty close to the scenario Spencer Wells paints in "The Journey of Man" and Cavalli-Sforza has in "The Great Human Diasporas". While I think Europe as a possible source of NAs is unlikely the article linked above suggests the two populations are related being members of subgroup X2.
" Finally, phylogeography of the subclades of haplogroup X suggests that the Near East is the likely geographical source for the spread of subhaplogroup X2, and the associated population dispersal occurred around, or after, the LGM when the climate ameliorated. The presence of a daughter clade in northern Native Americans testifies to the range of this population expansion."