Buyer returned working item claiming it was defective for a refund

[oilbird]

I recently sold a CD recorder on Ebay. The buyer paid me right away, and I sent it out the next day. I stated that I accept returns if DOA or different from described item. Two weeks passed, and today I got the unit back from the buyer! I was shocked, because I never heard a word from her. She claims it didn't record, so she returned it for a refund.

I tested the unit, and it works perfectly, records exactly as it should!

I contacted Ebay, and they told me to wait until she contacts them for a return and refund complaint, and then to give my side of the story. I don't want negative feedback since I have 100%, so I contacted the buyer and told her the unit works perfectly fine, no problems. I also told her that it's not fair for her to expect a refund for a unit that was exactly as described and 100% working.

I offered to return it to her.

Am I expected to give her the refund, even if she sent it back without notifying me and under false pretense?