Pinning the shift to an exact date like 1610 is silly, but I do agree with the basic premise of their argument. In fact, it's essentially why I chose to specialize in the history of the seventeenth century. Just from looking at the famous "hockey stick" graph of world population you can see that this was the period immediately preceding the shift into exponential growth - but what's fascinating is that populations actually declined in many areas in the seventeenth century, as did standards of living. Speaking of which, Eric Hobsbawm's concept of a "General Crisis of the Seventeenth Century" seems relevant here:
"a dip in global carbon dioxide levels caused by the abandonment of native farms across the Americas following the deaths of millions of indigenous people in the aftermath of European colonisation."
Wouldn't this suggest that the advent of native farming had previously caused a rise in global carbon dioxide levels, and consequently that the human epoch began much earlier?
http://en.wikipedia.org/wiki/The_General_Crisis