If true, this is very hard to reconcile with late (60kya) out of Africa and may be a smoking gun for pre-100kya presence of anatomically modern humans in Eurasia. From the paper:
The inferred demographic model confirms and provides quantitative estimates of previously inferred gene flow events among modern and archaic humans2, 3 (Extended Data Fig. 1). These include Neanderthal gene flow into modern humans outside Africa (3.3–5.8%) and gene flow from an unknown archaic hominin into the ancestors of Denisovans (0.0–0.5%). Interestingly, we also detect a signal of gene flow from modern humans into the ancestors of the Altai Neanderthal (1.0–7.1%). The precise source of this gene flow is unclear, but it appears to come from a population that either split from the ancestors of all present-day Africans or from one of the early African lineages, as significant admixture rates are estimated from San as well as Yoruba individuals. This introgression thus occurred in the opposite direction from the previously reported gene flow from Neanderthals to modern humans outside Africa
And:
However, it is clear that the source of the gene flow is a population equally related to present-day Africans and non-Africans (Extended Data Fig. 3). We conclude that the introgressing population diverged from other modern human populations before or shortly after the split between the ancestors of San and other Africans (Fig. 3a), which occurred approximately 200,000 years ago11.
The implications of this inference (if correct) for modern human origins are potentially monumental as they suggest a Eurasian modern human lineage (only detected in the Altai Neandertal) that diverges from other modern humans as early (if not earlier) than any two African ones.

If the new discovery checks out, it will no longer be possible to assert that the deepest split in our species, H. sapiens, involves African populations. A modest interpretation of these results would assert an earlier (pre-100kya) exodus of our species from Africa, and a more bold one would seek to re-examine the geographical origin of H. sapiens itself. I don't know if anyone is working on getting DNA from the progressive Neandertals of the Near East, but they should.

Things are bound to get more interesting.

Nature (2016) doi:10.1038/nature16544

Ancient gene flow from early modern humans into Eastern Neanderthals

Martin Kuhlwilm, Ilan Gronau, Melissa J. Hubisz, Cesare de Filippo, Javier Prado-Martinez, Martin Kircher, Qiaomei Fu, Hernán A. Burbano, Carles Lalueza-Fox, Marco de la Rasilla, Antonio Rosas, Pavao Rudan, Dejana Brajkovic, Željko Kucan, Ivan Gušic, Tomas Marques-Bonet, Aida M. Andrés, Bence Viola, Svante Pääbo, Matthias Meyer, Adam Siepel & Sergi Castellano

It has been shown that Neanderthals contributed genetically to modern humans outside Africa 47,000–65,000 years ago. Here we analyse the genomes of a Neanderthal and a Denisovan from the Altai Mountains in Siberia together with the sequences of chromosome 21 of two Neanderthals from Spain and Croatia. We find that a population that diverged early from other modern humans in Africa contributed genetically to the ancestors of Neanderthals from the Altai Mountains roughly 100,000 years ago. By contrast, we do not detect such a genetic contribution in the Denisovan or the two European Neanderthals. We conclude that in addition to later interbreeding events, the ancestors of Neanderthals from the Altai Mountains and early modern humans met and interbred, possibly in the Near East, many thousands of years earlier than previously thought.

Link