Kerbley,
Your sentiments are good but logic misses a point.
Overall(for the general public) Nuclear power is less dangerous due to the reaons you note. However, living next to the nuclear power station due to the localised effects of a leak would be much more catastropic. Eg. Fukushima.
You can stand next to a smoky barbecue and live but not be exposed to 10 GigaSeiverts 3m away.
I belieive there is a exponential fall off/ logarathmic decay in the intensity of radiation with distance.
PS: I think even my explanation is not that rigorous.
artical , page-13
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