Hoffecker suggests that the Strelets assemblages (the ones with Middle Paleolithic elements) are unlikely to have been produced by Neandertals, both because they persist until relatively recently, and because they are found at much higher latitudes than Kostenki, for example at Mamontovaya Kurya. I have some quite contrasting e-mail from a long-time correspondent, who offers that the Strelets assemblages are quite comparable to Szeletian, generally considered to be a Neandertal-produced "transitional" industry, and there is no diagnostic skeletal evidence to suggest these tools were not Neandertal-manufactured.
Personally, I would observe that there may be no predictive reality to the Neandertal-modern distinction, certainly not within this post 45,000-year timeframe. Genetics now provides good evidence that living humans descend from an ancient structured population with a significant fraction of Eurasian members. It is of course possible that some (or even all) European Neandertals still became extinct without issue -- the genes do not have "Neandertal" stamped on them. But the fossil evidence certainly supports the hypothesis that the "Upper Paleolithic revolution" in Europe involved some (i.e., enough to be visible) population mixture.
Whatever the genetic relationships of the hominids, there was evidently no information barrier between them capable of preventing the social learning of stone reduction sequences. The "transitional" industries are sufficient to demonstrate this information transmission. To be sure, there is a limit to which we can infer contacts from archaeological assemblages, which represent industries that in some cases lasted for many thousands of years. Just as for the genes, we cannot say whether these exchanges were sporadic or regular, large-scale or small-scale.
What does that mean for Kostenki? I think it means there is no contradiction between a long-term, widespread "transitional" industry and the idea that such industries have origins in the Middle Paleolithic. Both can be true. This implies things about the population of Eastern Europe, in terms of genetics, ecology, and the dynamics of information transfer. Where industries are interleaved at a single geographical location, this may say much about both natural ecology (climate fluctuations) and information ecology (social learning within groups applied to natural problems). The form of population contact is also relevant, but lies at a deeper level -- which technological patterns may or may not be able to address.