Still, 36 hours in a very high radiation environment is a very long time. also, I'm not sure how long the people in Chernobyl itself were there before being told something was wrong.

Hell, the soviet union didn't admit anything was wrong until a couple of days after, when the radiation was noticed by engineers in Sweden[1].

[1] http://www.cnn.com/WORLD/9604/26/chernobyl/230pm/index2.html