Well the effects of radiation were still poorly understood, but also there wasn't that much radioactive material left over in any concentration. And the gamma ray blast would appear superficially like normal burns from being near a firebomb until atleast a few days later.

Contrary to Fallout lore, most nuclear bombs dont leave much concentrated radioactive material unless it was done on purpose. You either need a shittier and smaller explosion with the same material, or you need a ground burst which reduces the effective blast area.

The US was on ground zero in under 2 weeks in Japan and couldn't detect anything over the background in radioactive isotopes.