I think you guys are missing one major fact here. When you pick up a fiction book, Ill say it again, when you pick up a fiction book, you are ignorant to think that it will be factual. Sure, it may have some facts, but ultimately its a lie, as per the definition of a fiction book.
so when you read a fiction book and it says "this is based on a true story", you have to realise the statement is fiction in itself. when you think what you are reading actually happened to someone, the impact of the events becomes bigger, and the story hits you on a deeper level as a reader.
I mean, if JK opened all of her books with "The following events are entirely factual and thoroughly researched using multiple sources." would you start to believe in the existence of magic?