Interesting, thanks for putting in the worthwhile effort to debunk that assertion. Clearly some hyperbolical claims have made their way into common wisdom and from there into model training data, which is unfortunate and feeds the conspiracy theories.
Because those claims go way beyond what is needed to support the current scientific viewpoint debated here. It's still true that homo sapiens is a startlingly recent species and that the visual characteristics which are so apparent to us (as a mainly visual species) depend on much more superficial genetic changes than one would imagine.
The bottom line, as I see it, is that there is good reason to apply a different standard for assigning (sub-)species status to a given population when we're talking about humans vs. other animals. If we think of a species as a branch of the evolutionary tree (i.e. a separate evolutionary trajectory), in the case of other animals, geographic isolation will, with overwhelming probability, lead to divergence over a long enough time. Human history shows that this is not the case for us humans. Whatever obstacle has divided us in the past, we managed to overcome it and mix our genes again.
Let's take the North Sentinelese people (possibly the most genetically isolated human population extant). It is believed that they were isolated from the main branch of humanity about 50kya. That's obviously a blink of an eye in terms of evolution, but maybe if we would be talking about chimps, scientists would have designated them as a subspecies. Probably not, but let's pretend that's the case. Should we then do the same? Taxonomically sanction that split and consign them to their own branch of the tree? It seems historically misguided, but also morally wrong. Like shutting the door on them. I guess this latter aspect is what's bothering some, but in my opinion it says more about them, than about science in general.