Its just one of those things people say a lot but has no real meaning to it. In a nuclear war, most humans would survive too. It would probably kill less than 1 billion people directly.
That having been said, the idea is based on cockroaches being much more resistant to gamma radiation and that living underground would also improve the chances.
But in the end, any nuclear event strong enough to kill everyone would also kill cockroaches. Fruit Flies are much more likely to survive.
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