I'm sorry about your buyer. Just think of it as it's his lost.
After the very 1st time they claimed I sold a fake item, all my listings were gone and I was no longer able to buy, or sell on there (though they didn't ban me, in which case, I wouldn't even be able to log in). After sending some angry emails and proof, I got reinstated. The 2nd and 3rd time when they claimed I sold a fake, my closet thankfully stayed intact, but it's just as aggravating.
Maybe next time, just include an authentication with all your sales, just to avoid situations like this. I know it's annoying when you have to spend money to do their job for them (having it authenticated), but it's for your own sanity. That's what I do now for all my items, 'cause I don't have a lot of trust in their authenticators.
I mostly sell loubs, and here they never made mistakes. I sold hundreds of them on posh (including over 500), and I help to authenticate them to poshers myself. even when they remove my CL listings cause someone reported them (it happened 2 or 3 times with the older styles), I always appeal, provide them more pictures, and they reinstall my listings. so their authenticators know the brand. but Gucci is not "my" brand, that's why I only sell them if I know they are from official distributor. so maybe it makes sense to spend money for authentication of all my Gucci to feel protected