Who mentioned a serial number? I thought Authenticity Guarantee just compared the item against the listing details. So if no serial number was mentioned in the listing, where are the buyer saying it doesn't match to?

If you do have to refund the buyer and you don't have the money in your eBay account then they will take it from your payment source. If that fails, then they will request you pay via other means. If you don't pay then they will eventually send the debt collectors after you.