My mother used to insist that cockroaches were "filthy creatures," which "spread disease." In fact, while scientists point out that the critters probably do spread disease via the microbes in the gunk they track through and get all over their legs and stuff, they haven't been able to actually pin any specific diseases on them.
In China, cockroaches are used as medicine. And lunch.
But not, as far as I know, in chicken nuggets.