I have two separate theories -
Originally, the first group moved into what was previously uninhabited (or Neanderthal) territory. So a small group of people are responsible for a general population. As they spread and expand, probably quickly, hitting previously untapped resources like abundant wildlife they fill the land. Anyone seeking to expand into there would be unlikely to displace them, unless they came with better tech and better weapons. Even then, they need exceedingly good weapons because an invader group would be outnumbered.
So it’s likely that the original inhabitants of say, North European plains and then Britain and Iberia were from a small source. Then they get overrun by the next wave - say, those with bows, or bronze weapons. or horses, etc., etc. But each such successful group also likely started with a small group that discovered something new and met with great success.
However, this pure genetic makeup of areas will be diluted by trade and war, both by taking advantages of the local entertainment and intermarriage. So the more cosmopolitan areas will se a much larger mixing of assorted source genes, while the “backwoods” would continue to have a more pure version of the original inhabitants. The Roman empire and subsequent mixing by trade and conquest would follow on the heels of Hellenistic expansion and then be followed by assorted invasions and trade, up to and including Muslim invasions that reached from the east to Vienna and from the south to southern France.
But each of those genetic analysis companies probably has limited means to track full family history. (i.e. none) they can go by generally published articles, but that’s about it. I suppose basically all they can do is rely on what distribution they see from the less cosmopolitan areas of the world - i.e. if our Basque village samples commonly have this more than found elsewhere, it must be a Basque trait. If many samples from Cambodia and surrounding areas have this, it must indicate Cambodian ancestry. If we see this in Greece and Sicily and Iraq, perhaps we can blame Alexander… But it does not guarantee any degree of geographical accuracy. Who knows who wandered where 300 years ago.
As for reliability of family trees - if anyone has lived in a small town, they would understand. In a small town - and they all were, until the advent of the train and auto added distance to anonymity - everyone knows everyone else’s business. If there were pedigree errors, then odds are the cuckold husband knew but chose not to deal with them. Shotgun marriages were common, so it was harder to escape the consequences of premarital sex. I would be more suspect of the family tree in the last 3 or 4 generations than earlier. There’s another factor, where a single mother brings a child into the new marriage. That possibly gets glossed over in some earlier family trees.
(In going through my family tree for rural England in the 1700’s, I find a lot of marriages followed by a birth a few months later (or even, preceding). Possibly not so much shotgun as a matter of “making it official” now that there’s a baby in the picture. )
