Mammoth extinction, humans not to blame?

There is a new paper in Current Biology, Genetic Structure and Extinction of the Woolly Mammoth, Mammuthus primigenius. The authors use recovered mitochondrial DNA (passed through the female lineage) to reconstruct the phylogeographic history of the species. It seems to me that the abstract is a bit more cryptic than it needs to me, but Eureka Alert has the meat of their paper in the form of a few quotes:

"In combination with the results on other species, a picture is emerging of extinction not as a sudden event at the end of the last ice age, but as a piecemeal process over tens of thousands of years involving progressive loss of genetic diversity," said Dr. Ian Barnes, of Royal Holloway, University of London. "For the mammoth, this seems much more likely to have been driven by environmental rather than human causes, even if humans might have been responsible for killing off the small, terminal populations that were left."

I'm skeptical of this interpretation. Not only are their data based upon mtDNA, which is not necessarily a good reflection of demographic history, but their interpretation seems to constrict the options for causation into an unnecessarily Platonic dichotomy, the environment vs. humanity. Remember that humans are part of the environment, so even if we aren't responsible in the first order for the extinction or expansion of particular species, our reshaping of selective parameters (e.g., draining swamps, generating a patchwork of "edge" environments within a forest, etc.) could have downstream effects.

The authors themselves note that mammoth expanded their range from two small isolated populations around 60,000 years ago. This suggests that like most species they are subject to fluctuations in effective size. The subsequent reduction in population may simply be the recapitulation of a demographic process which has been operative over the past million years, but during this down cycle there was a difference: humans had become far more effective predators. It seems more likely that humans did not deliver the coup de grâce to a species on the way to extinction, rather, our species was an unexpected parameter which changed the equation and eliminated the possibility of a future demographic bounce back. The paleoanthropologist Steve Mithen has shown through simulation that declining numbers due to climate change and heightened predation from efficient human hunters are the two necessary (though not sufficient alone) preconditions for the dynamic of megafaunal extinction. Though the anthropogenic extinction of the Cuban ground sloth may not be generalizable to all cases, I think it gives us a clue that modern humans were essential pieces of the puzzle over the past 40,000 years, there's no reason to pretend as if this is a speculative assumption.