The movie Fargo was shown as being based on a true story. That's what it says at the start of the movie.
After I saw that movie I thought about that and it seemed suspicious to me. Some time later I saw a program about the movie and in it William H. Macy (I think that's his name) when he saw the complete movie for the first time saw the "based on..." and knew that was a lie. He asked one of the Coen brothers (the directors) about it and he said that it's a movie and from the beginning to the end it's made up. He thought the movie would be more enjoyable if people thought it was true.
All "based on a true story" means is that at least one thing is true for example the story was set in Chicago and a city called Chicago does exist. A lot of people see that and think it's a documentary. It's a movie it's made up.