I think if you time your destructive interference to the source of the audio perfectly and cancel out the sound, you haven't gotten the whole picture. As sound travels away from the source it reflects off surfaces and some of those reflections also reach the microphone. Those sounds have traveled a different distance than the original source and are no longer timed with your interfering element. Imagine holding your hand to block your direct view of a person in a house of mirrors but you can still see them in the mirrors. On top of that these reflections won't contain identical audio as the surfaces will absorb different spectral content, so now even if you had infinite perfectly timed anti-signals for each reflection, your anti-signal has spectral content that is missing from the incoming reflected audio and now your anti-signal is a signal unto itself. In order to create a signal that perfectly cancels out all of the copyrighted audio you would have to have knowledge about the form and materials of the physical environment as well as the position of the microphone within that environment.
In the end, the solution does not have to be perfect. Just have to hide the song well enough so the content ID cannot be made. As you say, the sound that will manage to bypass the "inverted balanced-like filter" will be distorted and hopefully content ID is not accurate enough to recognize it.
