I'm not sure I understand the situation correctly. Did you return the headphones, which the store has already inspected and then refused to refund the payment, or did the store simply ask to have the headphones returned for inspection before they will issue a refund? If the latter, then it's certainly acceptable for them to want to inspect the headphones before issuing a refund, and I don't see any reason to be upset. In my many years of purchasing on-line using PayPal, I've only had to ask for their assistance getting a refund, one time, and that was quickly and easily resolved.
One more thought, having done a LOT of on-line purchasing over the years. Stuff happens, it's not unusual to have something arrive DOA. It's just part of purchasing on-line, but that's exactly why it's so important to deal with reputable vendors and always make sure you understand their warranty/return/refund policies BEFORE you purchase, and also why it's important to use PayPay Good and Services (not Friends and Family).
In any case, good luck with the return, and don't let this experience sour you on the LCD-4 headphones, they're worth the effort to find a good pair.