Genes have genealogies, just as populations do. Usually, a gene’s genealogy is the same as that of its species. For example, turtles have their own versions of hemoglobin, and the common ancestor of those turtle hemoglobin genes is some ur-turtle hemoglobin ( or is it turtle ur-hemoglobin ?) a long time ago. This is a stochastic thing: it happens when only a single version of a gene survives – after that occurs, gene trees and population trees match, at least until the next split.
But it ain’t necessarily so, especially in cases where two species separated rather rapidly, or when the splitting populations are large – even more so when populations haven’t yet speciated at all. When the gene tree conflicts with the population tree, we call it incomplete lineage sorting. For example, gorillas split off before humans and chimpanzees separated, but some of the human genome ( ~30% ) is more similar to gorillas than it is to chimpanzees. So, gene trees don’t match species trees very well among humans, chimps and gorillas – although they do just fine between, say, humans and bears.
How much lineage sorting would you expect from human populations that have been separated for, say 100,000 years? 250,000 years? Close to zero. Hardly any. So, can you use the fact that human gene genealogies do not match apparent human population splits to prove those splits never happened – that there had always been lots of gene flow between far-distant populations, say between sub-Saharan Africa and Siberia? Presumably using magic carpets?
You could, but only if you were a bird-brain.