Are all DTC firms underestimating African ancestry in Southern Europeans?

Several years ago a paper was published, The History of African Gene Flow into Southern Europeans, Levantines, and Jews:

Previous genetic studies have suggested a history of sub-Saharan African gene flow into some West Eurasian populations after the initial dispersal out of Africa that occurred at least 45,000 years ago. However, there has been no accurate characterization of the proportion of mixture, or of its date. We analyze genome-wide polymorphism data from about 40 West Eurasian groups to show that almost all Southern Europeans have inherited 1%–3% African ancestry with an average mixture date of around 55 generations ago, consistent with North African gene flow at the end of the Roman Empire and subsequent Arab migrations. Levantine groups harbor 4%–15% African ancestry with an average mixture date of about 32 generations ago, consistent with close political, economic, and cultural links with Egypt in the late middle ages. We also detect 3%–5% sub-Saharan African ancestry in all eight of the diverse Jewish populations that we analyzed. For the Jewish admixture, we obtain an average estimated date of about 72 generations. This may reflect descent of these groups from a common ancestral population that already had some African ancestry prior to the Jewish Diasporas.

At the time Dienekes had a pretty strong critique of the paper: the authors assumed that Northern Europeans were an unadmixed reference population, when in fact these populations may have had mixture from East Asians. He presented PCA plots which illustrated the fact that CEU (whites from Utah with British and German ancestry) sample were shifted toward Chinese in comparison to Sardinians. All these years later I think that in fact there is another explanation besides East Asian admixture to explain this: the Chinese themselves have some admixture from West Eurasians. The Sardinians are notably lacking in some admixture components common among mainland Europeans, so the West Eurasian admixture into Chinese probably is closer to mainland Europeans than it would be to Sardinians.

So what about the Sardinian admixture from Africans? The same dynamic might be at play here: old admixture from “Early European Farmers” into Africans might explain why they’re closer to Africans.

But let’s assume that the Sardinian admixture from Africans is legitimate. What does that mean for estimates of ancestral derivation from continental populations than you see in the DTC personal genomics firms that report ancestry results? It can only mean that among people of Southern European ancestry a few percent of African ancestry is being “masked” because it is part of the reference population set. This came to my mind because a half Cuban friend of mine had ~2% African ancestry. Reasonable. When I checked by running unsupervised ADMIXTURE he had ~4%. Then I noticed that the Sardinian reference set was often in the 1-2% range. One explanation for the discrepancy then would be that a few percent of African ancestry in his genome was simply swallowed up by the reference population in the supervised learning framework.