Some pre-amps and dacs have polarity switches. It inverts the stereo signal's "absolute polarity" It works on both channels. It has no effect if the music signal is completely symmetrical. But a lot of recorded music isn't. And if it isn't, it can cause compression when played back. Try reversing the speaker cables on your speakers. On some music, you can hear a degradation of sound. Music companies don't all record alike. It's like a 50-50 shot. So a polarity switch can make a difference. (although slight to some)
The last time I checked, Caveat emptor was Latin, not Greek.
But see what happens when you're happy with your headphones so you don't come into the headphone forum? You miss stories about ebay scammers who ....scam. Hmm, that fell dead, but this story is complete news to me.