How does a credit score service know which of the dozens of John Does you are on Facebook?

The only ways in which this can work is a) you have a pretty unique name on FB or b) you have to give your FB name on your credit application (if I'd see this on a form, I'd just tell the bank guy to forget everything and walk out).

Of course, this opens a possibility for manipulation - either you use someone else's clean FB page, or a malevolent entity creates a profile in your name, or you yourself have one "clean" profile and one "real" profile which many people already do to hide their pot smoke pics from potential employers.