Actually, I’ve always viewed this song as illogical. I mean, if Meatloaf already knows that he won’t do "that" for love, why is he singing "I would do anything for love". Surely given that he is already aware of his personal opt out, he should sing "I would do almost anything for love".
Let me explain it a touch more simply. In the diagram below (nicked from Wikipedia) we can see clearly that "anything" in this case cannot mean the complete set of options (U) since Meatloaf won’t do "that". "That" clearly is the object A, so "anything else" is the complement of A (AC) and therefore (U) cannot be "anything for love" because it contains the object A which Meatloaf is claiming is the complement of U (which it clearly is not).
Got it? Sadly Meatloaf didn’t.