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.