Nothing subjective about it.. "based on a true story" means just that - based on the story.
It does not mean, "The faithful re-telling of a true story".
One could argue we lose history because of it, but on the other hand many of our beloved fairy and folk tales (even before they've been Disneyified) are 'based on a true story'.
Dracula and Vlad the Impaler come to mind.
RE: Some Facts About the Real P.T. Barnum That Do Not Appear in The Greatest Showman Movie