I beg to differ with you on that. One of the isotopes in fallout is iodine 131. The body readily absorbs it and it decays inside the body. It is very dangerous. Additionally, Strontium 90 is often mistaken by the body for calcium. It is stored in the bones and then it decays.
When the trinity shot when off some of the fallout came down in Ohio where Eastman Kodak had their paper mill for their film. Needless to say the paper was ruined because when the film was created little spots developed on it.
Ironically, when Ranger Able went off in Nevada some fallout came down in Rochester, NY. Which is where one of Eastman Kodak's main warehouses was. It developed spots on the film. Kodak sent a 4 word telegram to the AEC that just said "What are you doing?"
No news here. The main effect is the blast. There was fallout coming down all over the planet for decades, from hundreds of nuclear tests, many of them a thousand times bigger than the atom bombs Iran is building.