If it was recorded by a microphone in a space, then that won't work. Time and frequency inaccuracy in playback by speaker, sound reflections, and inaccuracies in recording by microphone all contribute to a signal. The original can be recognized, but simple subtraction will never remove it.
But keep in mind the goal isn’t perfect removal. You only need to disrupt the audio hashing algorithm.
This is untrue, things like Fourier transforms can account for those variables.
I'd love to see a demonstration of this. (not of a FFT, but use of one to remove one signal from another)