The only thing that needs to be "true" in a movie so they can state it is "based on a true story" is to have a real name or place regarding a particular situation. Other than that, they can make it up as they go.
If someone makes a movie and put "based on a true story" & it's not true.. Well they can be sued, all kinds of bad things can happen. So yes, the movies that say "true story", really are true. But keep in mind that it's not exactly how it may have happened. They can add to it or take things out of that story. But the general storyline actually happened.