pedantic correction: One billion Facebook accounts are accessed every month. No third party established that each account corresponds to a unique person.
Considering the vast amount of complaints towards Facebook regarding privacy concerns, do you really think it would be in the best interest of those users to allow third parties access to all of their data to "verify" that?
no data to support, but I'm pretty sure the amount of people with multiple facebook accounts is pretty small(at least comparatively to things like e-mail adresses)