Funnily enough this is spot on. There are Native Eurasians, Native Africans, Native Islanders and Native Europeans but there is no such thing as a 'Native American'.
In fact not a single form of ape life is native to any part of the Americas at all nevermind Human life. The Americas are isolated and unique in that regard. Europe, Asia, Africa and Oceania all have their own native ape life from monkeys to great apes (including humans, spaiens, neanderthals, Habilis etc.)
'Native Americans' are descendant of various ethnicities of Asians who marched across the Pacific during the ice age and the rest who sailed across and settled in the Pacific islands. So The Americas belong to ALL humans of any and all backgrounds because they're both alien continents and thus as the meme states: "It's free real estate."