The phrase based on refers to the basis of something. If someone writes a book on the basis of factual events, the book is "based on a true story."
I think the new, mangled idiom assumes that the root word is base, i.e., the bottom surface of something, or a floor. The floor serves as a "launching point" for new content, which leaps "off of" it. So in the example above, the book is not entirely true, but it uses reality as its anchor as it explores new dramatic possibilities. Not to justify the new phrase, which is really awkward to say. And besides that, this etymological study, as usual, is totally madeupical.