My favourite is the story that there was mass panic over a radio broadcast of War of the Worlds where everyone thought a real alien invasion was happening. I heard this story as a kid and really thought this was a cruel prank played by the radio station.
In reality, they made it clear at the beginning of the broadcast, and twice during, that it was fictional. Not that many people were listening and most of the people who were, were aware it wasn’t real. A few idiots freaked out and it somehow turned into a story of mass panic. It was propaganda by newspapers to discredit radio.
Similar to the Strangelove example - although not about history - know what medical professionals consistently say is the TV show which not only had the most accurate medicine, but also best depicts the social paradigm of working in the medical sector? Scrubs.