Finding fake roots

I haven't watched much of Henry Louis Gates Jr.'s Finding Your Roots series. It seems like Gates has kind of created a mini-empire in genealogical series on PBS. More power to him, but it hit diminishing returns for me a long time ago. But I see clips online here and there. And something which I saw really kind of disturbed me. From what I can gather Gates regales his subjects with their DNA results, and tells them their ancestral quanta fractions. Nothing too amazing. But it seemed clear to me that when Gates referred to "European", "Asian" and "African" ancestors, he was communicating to the audience that these quanta really represented those exact populations! I assume that the geneticists Gates works with explained to him the falsity of this typology. I also understand that the television format results in natural license. But Henry Louis Gates Jr. has produced lots of these shows now. He has the leisure to unpack the concepts for the lay audience. As it is, it seems he is repeating misconceptions of model-based clustering algorithms. Misconceptions mind you which persist even within the biological community. But that doesn't make it any better. For those who aren't getting the essence of what I'm saying, above are my 23andMe results. I'm 60 percent European, 40 percent Asian. But those fractions were produced assuming that I could only be a combination of Northern European, East Asian, and West African! Computational algorithms do not return results of the form "I'm sorry, but the input is going to generate useless output." So they came back with these results, which are highly misleading. Adding another reference population from South Asia makes the results much more plausible. The take-home is that the terms for each quanta are only mnemonics. They should never be taken literally.