"But It Really Happened!" is an exceedingly weak name. With a title like that, I expect the trope to be about someone who has a fantastic adventure, only to be unable to convince anyone around him that his crazy experience really did happen.
"The Tasteless But True Story", on the other hand, says exactly what this trope is about.
"From the director of a long list of exploitation films, comes the tasteless but true story of how one man screwed a goat."