Another thing you can do is to add pain to the second part of it. Attackers want the list of valid usernames, so they can then try to guess or brute force the password. You can put protections in place with that as well, whether they are lockouts or multi-factor authentication, so even if they have a valid username, it's much harder to gain access.

Since the authenticity token is stored in the session, the client cannot know its value. This prevents people from submitting forms to a Rails app without viewing the form within that app itself. Imagine that you are using service A, you logged into the service and everything is ok. Now imagine that you went to use service B, and you saw a picture you like, and pressed on the picture to view a larger size of it. Now, if some evil code was there at service B, it might send a request to service A (which you are logged into), and ask to delete your account, by sending a request to http://serviceA.com/close_account. This is what is known as CSRF (Cross Site Request Forgery). If service A is using authenticity tokens, this attack vector is no longer applicable, since the request from service B would not contain the correct authenticity token, and will not be allowed to continue.