The blockbuster discoveries of 2010 in human evolution and genetics flows from comparisons of ancient Neanderthal and Denisovian whole genomes with those of modern humans. The studies concluded that all Eurasians have a roughly 1%-4% Neanderthal admixture with no clear geographic spread (relative to Africans) and that Melanesians had an additional significant Denisovian admixture leaving them with about 5% Denisovian genes and about 8% archaic human genes all together.
The Neaderthal and Denisovian bones from which the ancient DNA was extracted was from the Upper Paleolithic period during the era in which humans and Neanderthals were known to have shared territory in Europe and the Middle East.
One possibility that I haven't seen explored anywhere is that admixture did happen, but that we have the direction of the genetic link wrong. Why isn't it possible that an Upper Paleolithic Eurasian modern human population made a 4% contribution to the Upper Paleolithic Neanderthal population from which the ancient DNA samples were drawn, instead of the other way around? This would, among other things, provide a simple explanation for the apparent uniform admixture levels in modern Eurasians - it would simply reflect that fact that all Eurasains were genetically fairly close to the Out of Africa founding population ca. 30,000-50,000 years ago, but had by that time already acquired the genetic mutations that distinguish Eurasians from Africans.
Also, while this seems less likely, couldn't it be possible that one group of early Asian modern humans traveled to Melanesia, while another part of the same group broke away, ended up in Southern Siberia, and contributed about 5% to the genome of the Denisovians? The distribution of Y-DNA haplogroup D, which is found in Tibet, Japan and the Andaman Islands, among other places, is suggestive of the possibility that early modern humans in Asia could have had migrations on this kind of geographic scale could have taken place, without leaving traces in intermediate areas. The population associated with Y-DNA haplogroup D itself, however, would be a poor fit because there are no traces of it in Melanesians. One would have to imagine this migration involving Melanesian specific lineages.
If these scenarios is correct, it culd be proven by showing that the admixed genes seen in these late archaic humans would be absent in older ancient DNA from archaic humans. In the absence of this kind of evidence, one would have to look for signs that the apparently archaic human genes have a sufficiently shallow age depth to derive from a modern human subpopulation.
Since archaic humans were experiencing a population crash at around this time as their species was well on its way to extinction after contact with modern humans, the number of admixture events necessary to leave this kind of genetic trace would have been quite a bit smaller than it would have had to have been to produce that much admixture in the other direction.
Maybe there is some key fact that I'm missing that rules out this possibility. But, it seems to me that it bears consideration as at least one of the viable models to explain the data until proven otherwise.