To be clear, are you saying the more accurate statement would be: "Neandertal chromosome segments found in all tested non-african populations, and some tested african populations"? (Which, when you put it that way, seems like a somewhat weird distinction to make.)
edit: I followed the link upthread, but it was only to the paper abstract. Is the full paper available for free online somewhere?
edit2: It seems the distinction might be no neandertal geneds found in sub-Saharan African population samples?
Yes, your more accurate statement is correct.
> "It seems the distinction might be no neandertal genes found in sub-Saharan African population samples?"
Regarding the Sub-Saharan distinction, the article text's terminology describes haplotype B006 as "virtually" absent from Subsaharan Africa. They then explain this as meaning that 6 out of the 1420 subsaharan samples contained B006, including 5 from tribal groups in Burkina Faso. They explain this away by supposing that these tribal groups must have historically interbred with north African groups, which is not an unreasonable guess, but I am sure it is also true for many other subsaharan groups as well. North African incidence rates of B006 are comparable to the middle east and Russia and higher than China.
So, 0.4% of sub-saharan samples contained B006, but not none. Also, north-western mexico, east south america, east china, siberia and indonesia all have similarly extremely low incidence rates, but no explicit mention of these areas is made in the paper, it's just seen in the data. Only subsaharan africa is called out for special mention. The highest rates of B006 are in western Canada - greater than 25% in some areas.
There is also a separate problem of the circular argument due to the inherent selection bias of brute force digging through the data sets looking for a gene with these characteristics. It's not like they started with a gene they knew was neandertal only, researchers sought out a gene in the single sequenced neandertal sample which had lower modern african incidence rates and from that concluded it was a non-african sourced neandertal gene, then turned around and concluded the reverse, bringing the argument full circle. That's another problem but I'd just as soon not get into that since I would much rather assume that is all good and only focus on the very misleading titles that are going around in articles about this paper.
There have been studies showing that individuals from two different races, for example Caucasian and West African, are usually more similar genetically to some members of the other race than to some of his own. What is meant by this? How is it possible considering that people of the same race share much more recent ancestry than people of different races? Then later you see graphs showing genetic clusters, how can there be clusters if people aren't more similar to one another for being of the same race? Did they use mixed race individuals for these studies? Are the parts of the genome that make two people look more similar to each other random parts or specific ones, what do these parts do? And finally in the global similarity section of 23andme, one can see the groups he's most related to, how is this possible?
I'm not up to date with the racial arguments you mention. I know there was something of an obsession 50-100 years ago with trying to establish a scientific basis to justify racism, imperialism, land theft, sterilization, imprisonment and subjugation of non-european peoples and there are still vestiges of those assumptions in a lot of research.
With the claim that "individuals from two different races, for example Caucasian and West African, are usually more similar genetically to some members of the other race than to some of his own", I have heard similar claims but how I understand it is they are not saying randomly chosen individuals from two different groups are more similar than randomly chosen individuals from within a group, but are comparing diversity of individuals within a group to diversity of group averages between groups. In other words, the claim is that the variation between two related individuals is greater than the variation between two unrelated groups, taken as averages. You are correct that if the claim is being presented that individuals between unrelated groups are more related than individuals within related groups, the argument doesn't make sense. It would not be surprising though if it has been presented that way in some articles and then repeated until it became a self-propagating myth. And again to clarify, I'm not up to date with any of those arguments, but just speculating on what might be going on.
I'm not arguing any position, just trying to understand without being very familiar with genetics or statistics. Maybe I've read the studies the way you presented it but my simple mind interpreted it that way. I'm guessing there is a huge flaw in what I drew but I don't see it, I can't picture in my mind what you meant.