That's putting it a bit strong, after all Marie Curie died of "aplastic anemia brought on by exposure to radiation" in 1934. https://en.wikipedia.org/wiki/Marie_Curie
And "actress Midori Naka, present during the bombing, was studied extensively for radiation poisoning. Her death in 1945 was the first to be officially documented as having been caused by radiation poisoning" http://www.news-medical.net/health/Radiation-Poisoning-Histo...
So they might not have had good statistics but they certainly had reason to be cautious.
Of course radiation is also used to treat cancer, there is a good side to many things.