I wouldn't give anthropics too much credit here. The sources I've read place direct fatalities from total nuclear war in the hundreds of millions, with deaths from secondary effects (mostly global disruption of food supplies) possibly in the low billions: an unprecedented scale of fatality, but not an extinction-level event.

(Note however that the OTA study linked through the FAS site took place in the late Seventies, a relative low before the Reagan-era arms buildup.)