Did meteor kill the mammoths?

About 13,000 years ago, the giant mammals of North America began a rapid slide into extinction. Why? Climate change and overhunting by early Native Americans have been blamed. A recent theory I liked blamed a meteor impact, based in part on the finding of tiny diamonds that might results from such an impact. A new analysis says these findings were wrong: the "diamonds" were just natural carbon lumps. The original scientists, though, are sticking to their guns.
I never liked the overhunting idea: Africans with hunting technology similar to that of Native Americans never made a dent in their continent's equivalent megafauna (elephants, rhinos, etc.) Hunting plus climate change might have done it, but it still seems inadequate to me.