Fair use is an affirmative defense. Others can still sue you for copying, and you will have to hope a judge agrees with your defense. How do you think Google v. Oracle would have turned out if Google's defense was "no your honor, we didn't copy the Java sources. We just used those sources as input to our creative algorithms, and this is what they independently produced"?

If I take a song, cut it up, and sing over it, my release is valid

"valid", how? You still have to pay royalties to the copyright holder of the original song, and you don't get to claim it as your own.