Uh, no. A study just published has confirmed the unfashionable but extremely plausible theory called Pleistocene Overkill. In summary, as our ancestors left Africa and spread out, first over Eurasia, Australia, and then to North and South America, they slaughtered and most probably devoured most of the the large animals. The totals are Africa 18, Asia 38, Australasia 26, Europe 19, North America 43 and South America 62. The extinctions correlate strongly with the arrival of hominins, and are far better correlated with our arrival than with climatic events.
The relationship between hominin palaeobiogeography and extinction magnitude is striking, with universally low extinctions in sub-Saharan Africa (maximum 13%), where hominins and the megafauna have long coexisted, but widespread exceptionally high extinction in Australia and the Americas, where modern humans were the first hominin present.
I still think Pleistocene Overkill would be a great name for a heavy metal band.