@merk There are a lot of other websites giving you that feedback, this is not only Facebook. For example Github, Gmail. 
In Gmail they ask you to enter your email + firstname + last name you used during registration process, if we want more security we can ask for username along with the email. 
I don't see any problem providing this feature to anonymous users given the fact we provide the reset password feature to anonymous user already. It is useless to equip a house with reinforced door if you let your windows opened...