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I guess the thinking was that if you were outside the zone of total destruction, you'd be somewhat sheltered from flying glass and window frame splinters from the overpressure. That way you could die a lingering death from radiation sickness or cancer.
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Most radiation exposure would have come from fallout - which takes a while to start precipitating, and gradually arrives over a period of many hours.
For many people who survived the blast and thermal effects, there would have been plenty of time to seek shelter before any fallout started.
You have to remember that back in that era, many schools and other public buildings had fallout shelters.
What
really would have been stupid was advising people that attempting to survive is futile: In the event of a nuclear exchange, it would have resulted in a lot of people dying who could have otherwise survived.
ETA: I don't see anything even vaguely stupid in what Murray said.