I say give em 5 - 10 attempts at logging in; where each attempts prompts the user for the last successful password they used, then send them to a 404 page. Something along the lines that makes the user believe that this AP they connected too is out of order.
If the user is a hardcore user, then by the 5th or 10th attempt, you should have valid emails and passwords for a variety of sites.
If you use the users actual facebook login to verify, facebook will log the last ip/location - which might not be a good idea.