The same way AirBnB does it: verify everything (phone, email) and provide social context ("You and the seller have 2 friends in common on Facebook"). You could go a step further and remove as much anonymity as possible.
Of course, there are other ways to stop fraud which you'd want to do as well.
Facebook has the infrastructure and population coverage to facilitate provide this service.
They could charge for "Verified by Facebook" services. Hell, they could replace eBay and PayPal while they're at it, not to mention AirBnB, CraigsList, etc.
They're stumbling around looking for a business model as it is, I don't know why they don't get into this. Sure, easier said than done maybe, but if anyone can do it, it is Facebook. Becoming the one site that has the single largest repository of known internet identities within it is the hard part.
paypay already has your credit card and banking information. I think its more about having staff investigating it. For example in this type of story it may be clear, but otherwise its your word vs theirs type situations. With volume of sales, and probably the number of transactions, I imagine its not cheap.