You know, I've often heard the bit about cockroaches surviving whatever destroys us, but I have to wonder if that little factoid comes from the same people who discount the effect of the Sun when they discuss global warming.
Yeah, they are not thinking things through. They say it because the roaches can survive the radiation, but they forget that they are completely dependant on humans for survival. German roaches would be worse off than German Shepherds if we were gone.