I'm surprised they don't mention Marie Curie. She died from it and it was way earlier than the nuclear program in the US.
While long term radium exposure has been known to be hazardous by the 1930s, and Curie's work had been suspected at the time to have affected her health, I estimate that contemporary thinking would have been to avoid exposure to radium.
Conversely, I do not think that acute exposure to radiation happened enough before World War II to have any kind of safety thinking around it.