Accused unfairly of selling fake iphone on ebay what do I do?

I fairly recently sold an iPhone on ebay for about $700. When I sold this iPhone, in the ad I said that I didn’t accept refunds, and that the iPhone was new and unused for any reason other than to take the pictures for the auction. About a week after I sold the phone, the buyer contacted me accusing me of it being fake. I had absolutely no reason to think that it is fake, it had all of the iphone logos, and to the best of my (limited) knowlege it was an iphone. I asked the buyer to give me proof of the phone being fake, and he told me that he wasn’t able to do that, and I told him that I would not give him any refund without the proof. After arguing with me for a wile, I got a letter signed (supposedly) by an AT&T manager saying that it was not a genuine apple product. It seemed strange to me that the letter came after he told me so many times that he was unable to get proof so I called the AT&T store where he supposedly had the letter signed and they could neither confirm nor deny the authenticity of the letter. To me it seemed that the buyer was just trying to get a refund because of buyer’s remorse and my return policy. Since the phone has been used since I sent it out, it is now worth less money, so if I refund them I will be loosing the depreciated value of the phone, the ebay listing fee, the shipping fee, and the paypal fees. My question is what should I do here? I was thinking that since the time that the buyer has to file a claim with paypal is up in about a week, it might be best to just not respond to them until the time period runs up so they can’t try to do what they are doing.
I also don’t know very much about iPhones at all, so in the event that it was a fake i’d like to know if there is anything that they can do to me other than dispute it with paypal or leave me negative ebay feedback , just to cover all of my bases, if they are able to somehow take it farther i’d like to know what my options are so I could just cut my losses. I figured that the money I would loose isn’t worth taking the hassle of them trying to report me for something, but at the same time i’d really like to not get screwed over.