What else would the phase inverter change, then?
I wish I could be as confident as you)
There are two ways to switch the phase - analog and digital. I have already described my opinion about the analog version: it is impossible to put a pure experiment here.
But the digital is also full of mysticism. I have my own experience in this matter. The code of any software player can be divided into the part that deals with the actual decoding of the sound and the part that creates the user interface (buttons, menus, etc.). It is natural to think that the sound is affected only by the first part of the code, the rest can be changed as you like. Once, for certain reasons, I decided to check this statement, and made several versions of the same type of software mp3 player for Windows with different interface. To do this, I used the "Multimedia builder". As a result, the player with the most complex interface - with a clock, track time, the ability to visualize music and many more, sounded the most muffled and and generally the worst of all. The most pure music played through a minimalist version of interface in which there was nothing at all except "open file" and three buttons. The experiment definitely indicated that:
- The sound is affected by the entire code, not just the part associated with encoding and decoding the audio signal.
- The simpler the software, the better it is for the sound.
Both conclusions are mystical, but I got used to such things. And I have to say that to me the difference was quite significant. Therefore, when I am told that the phase inversion in the software player makes a difference in the sound and this proves that the phase is audible, I answer that unfortunately this does not prove anything. We don't know how the piece of code that responsible for inverting the signal would affect the sound in case it didn't invert anything, but was simply added to the player code in a way of interface or so. And we also don't know is the code in inverter part technically correct, mistakes are what make us human.
I have found this mp3 player, you can try its sound if you have Windows -
https://backtomusic.ru/wp-content/uploads/2017/12/play.zip