I guess I agree that a recording with the polarity wrong has no affect on the phase of your system. The + signal (and minus) of DC current going through your hardwired system cannot be reverse solely based on music encoded on a piece of media, whether, CD, LP, or Tape. That would defy the laws of physics.
If you had a recording with multiple microphones, where some microphones were in phase and some out of phase, some sounds may cancel out in part, which is why the recording sounds off. You system won't be feeding post positive and negative current to both speaker terminals at the same time. I hope you agree that is impossible.