The authors interpret the new result from HST as placing a lower boundary on an introgression from Africans to Neandertals at more than 290kya, which explains why Africans are genomically closer to Neandertals than to Denisovans.
Of course, when one looks at the mitochondrial phylogeny, it has the form:
(Denisovans, (Neandertals, Modern Humans))
Within the Modern Humans, Eurasians are a branch of a tree which is mostly African. This has been interpreted for decades as evidence for the Out of Africa hypothesis for the origin of Modern Humans. But, within the phylogeny as a whole, Modern Humans are a branch of the Eurasian tree. This has not (why?) in general been interpreted as evidence for Out of Eurasia for the common ancestor of Modern Humans and Neandertals.
It seems to me that this hypothesis, that Modern Humans and Neandertals stem from a non-African ancestor (a non-African population of H. heidelbergensis, for example), has much to recommend it.I guess the science isn't quite settled yet.
Eurasia has twice the size of Africa and has been home to hominins for ~1.8 million years. It was inhabited by diverse hominins, and thanks to blind luck we discovered that as late as a few tens of thousands years ago, it also sported two of the populations that split off before anyone else: first H. floresiensis, and second Denisovans.
While a North African source of modern humans is plausible, the data seems to favor a Eurasian origin of the (Modern Human, Neandertal) ancestor.