The hinge point in paleoanthropology right now is the European Middle Pleistocene. Neandergenes don't fit fossil record. That is, Neandergene analysis seems to rule out substantial Neandertal ancestry from Atapuerca et al. Instead, Neandergenes appear to derive from Africa after 250-400 kya. Is Atapuerca/Petralona/Arago a dead end? Or can we find a model that fits data and allows some substantially deeper Neandertal local ancestry? And while we're at it, can we get any Denisovan ancestry to be consistent with Asian Homo erectus?
The Denisovan genome analysis seems to rule out any substantial mixture with Neandertals...but Okladnikov is literally 3 days' walk. There's simply no biogeographic barrier. The populations need not have been here at same time, but if not where were they? If we can't resolve the European Mid Pleistocene problem, fossils may never help with Denisovan problem.
Basically, Hawks is pointing out that three groups of fossil remains of ancient hominins, (1) the non-Neanderthal archaic homo of Europe in Atapuerca (Spain), Petralona (Greece), and Arago (France) from ca. 300,000 years ago to 200,000 years ago (I call them archaic homo out of respect for Hawks who states in one post: "The "Homo heidelbergensis" model is in such utter disarray right now, I'm not sure many paleoanthropologists have realized the full extent of the problems. You should know that I don't believe in Homo heidelbergensis, never have."), (2) the Neanderthals whose European centered range extended to as far east as a few days walk from Denisovia in Siberia in a find from 38,000 to 30,000 years ago, and (3) the Denisovian remains whose affiliation is unclear but genetically disjoint from Neanderthals according to the ancient DNA, don't seem to have had any known ancestral or admixture links to each other except as possible link of Denisovians to either Asian Homo erectus (or something else, such as population (1) in this list?). As he noted earlier the same day in a tweet: "With Ngandong date change last week, no H. erectus fossil is late enough to be part of a Denisovan population."
The main traces of the Denisovian genome in modern populations appear to be mostly restricted to Melanesia and populations with Melanesian admixture, rather than having a global distribution, and seem to be absent in North and Central Asia which are the source of the Denisovian fossils that were the source of the Denisovian genome, and those fossils aren't extensive enough to allow for any serious reconstruction of their large scale appearance. (Hawks is skeptical of claims that immune system genes bearing similarity to the Denisovian genome are really Denisovian in origin.)
Dating of fossils from India has also muddied the story of Eurasian hominins in the early and middle Paleolithic.