I have seen fiction outright stating, "This is a true story" - i.e. Fargo, or the rather-less-good "The Sleep Experiment". The former at least has great production values and is actually taking inspiration from real events. The latter is 110% made up.
In the case of Fargo the cohen brothers chose to make a movie in the “real crime story” genre, and that title card sets the tone. Any overlap with actual crimes is almost beside the point. (As a viewer this really bugs me — there is such a thing as truth!)
UFO sightings were a real common thing in Minnesota, so in the show a real UFO comes, because it’s people telling the story as they saw it. The true part is that people truly tell the stories, and in that sense, since they told this story it truly is a true story.
Stupid show. I watched the entire first season waiting for the guy to turn out to be an alien and then I find out it's in the second season and it's just a UFO sighting.
There's like a gradient of "truthiness" in movies that ranges from "This is a true story" to "inspired by real events" (which is the least reliable of all).
Well based on a true story has no real percentage of trueness. Cocaine Bear is based on a true story. It might be more correct to say inspired by a true story but it is based on a true story.
Based on a true story just means someone somewhere said something like this happened. Bloodsport is a great example of a movie that is based on a true story but that true story turned out to be entirely false.