IMHO "based on a true story" applies also if you're sticking to literally true facts but intentionally omitting other facts and misrepresenting in order to get

IMHO "based on a true story" applies also if you're sticking to literally true facts but intentionally omitting other facts and misrepresenting in order to get an entirely opposite impression. I mean, you're twisting the story, but it's definitely still based on that story; and only facts can be true or false, but the interpretation, ethos and "spirit of the truth" is essentially arbitrary; you may consider that the facts drive home a particular conceptual point, but everyone is free to try and use them to drive home an entirely opposing conceptual point. It's a lie if the facts are not literally true, but representation and alternate interpretations of them is permissible even in nonfiction, and absolutely fair game in fiction.