There's really no excuse for based off (Their favorite classic movies are based off old fairy tales) or its alternate form, based off of (Dr. House is based off of Sherlock Holmes). Whoever coined based off was just fooling around or talking too fast. It subsequently caught on, and now there are those who defend its legitimacy.
Everyone knows the correct phrase, based on, which has been around forever. But somehow, on became off, or worse, off of—a compound preposition that all English authorities reject as substandard (see off of).
The logical conclusion is that anyone who says "based off" doesn't know what based means. As a verb, to base means "to form a foundation for." The noun base refers to the underlying part that something rests on, not off.