It's a scam, or con as many people say. Some buyers simply try to trick the seller into giving them a refund. If they state that they will give you a negative feedback if you do not refund them - click on the "report a seller" link if you have one (I am answering from the US where we do have that feature).

It's buyers like this that make selling on eBay so unpleasant.

With no proof, I wouldn't pay. I don't know what ebays stand is on this but without proof, I can't image they would demand a refund from you. They should have insured the item and that should have covered the damage as i see it. You are off the hook when it leaves your hands. If they overpaid, that is their problem. That's what happens when the bidding gets going and one should only bid what one is willing to pay. I think they are scamming you.

They still have plenty of time to open a case. Hope you contacted them using ebay messages so ebay can see what you said?

You have not heard because its a Con. They should take this up with Royal Mail, not you.

UK

This was about 3 weeks ago so i don't think much can happen now anyway but hey

I sold something on ebay and to be fair I think they did over pay a little but the auction started at 99p and I had two people fighting over it at the end so anyway it took the buyer a 10 days to pay for the item after I sent email and ended up sending a non payment I sent the item iff all packaged up in bubble wrap and in a box a week later I got an email saying the item had arrived smashed I said I was very sorry about this and asked if they could send me photos of the damage so I could give them a refund and get my money back from Royal Mail I have had no response to this