I watched Fargo by Coen brothers a while ago, and I remembered clearly that the intro says "based on a true story". However, when I searched the movie online I found that the plot was entirely fabricated.
Usually the producers will issue a disclaimer such as "all characters are fictitious" to avoid potential legal issues, but Fargo is doing the other way around. Are there other movies claimed to be "based on true events" but actually are not?