2. After the data has been downloaded and parsed, an automated system checks each one of them against the Facebook internal databases to see if any of the email addresses and hashed passwords match valid login information on Facebook. We hash each password using our _internal password hashing algorithm_ and the unique salt for that person. Since Facebook stores passwords securely as hashes, we can't simply compare a password directly to the database. We need to hash it first and compare the hashes.
This seems to imply Facebook is rolling their own cryptography...
Its also very self-serving of them to recommend Facebook Login without even mentioning OpenID. Facebook Login in no way improves the security of your Facebook account, in fact I'd argue its likely to do the opposite due to phishing etc. It seems pretty transparent they're pushing an agenda in the guise of security advise, here.