But the answer that one would conclude is "so that private citizens can't find out all the shady things we're doing with radioactive stuff".

I presume that was the policy even before Chernobyl. The US did not run an entirely clean nuclear program, but the USSR was worse (perhaps because ordinary people in the US could have Geiger counters, and so the powers that be knew that they were less likely to get away with spilling radio emitters).