Sidenote... If you use Facebook's free native plugin for Unity to authenticate the person's login... well since I wasn't able to do the Facebook login thing myself and people kept asking about it I added an extra option to my kit where, if you are CERTAIN that a user is who he says he is then you can simply replace my call to AttemptToLogin() with DoTrustedLogin() and pass along the user's email address. My kit will then allow you to log that person in without a password. Thus, as long as the email address in his WordPress account matches the email in his Facebook account then you can log them in via the Facebook native plugin , get the user's email address from FaceBook directly and then pass that email to my function to leg them in that way.
Of course, by the same token, you can log them in via Facebook and then, if they don't yet HAVE an account on your site simply auto complete the email address from the FaceBook asset and submit a registration from my kit like normal. Thus also ensuring the email address matches :)
Slightly more roundabout than I would like but at least this way you are using Facebook's own code and you are sure it will always be up to date and work as Facebook intended for it to work AND you get the added benefit of my kit no longer needed the login page / password to be entered. Only problem here is that if they ever change their email address then they will need to make sure they update it in both places in order for FB login to succeed...
Hope that helps. :)