Turned down? I’d walk out of the interview without a courtesy. I wouldn’t even work somewhere that PP was entirely voluntary, since any company that use it at all clearly isn’t serious.
I like everything you said in your response, although I see headphones with the right kind of music (ambient or liturgical, absolutely without beats and absolutely not a vocalist) to be equivalent to silence. It’s been a long time since software offices operated under library rules. Hallway conversations, foosball yelling, these break concentration.