I read an article about Facebook 2-factor authentication fail on The Hackernews earlier today.
In short, Facebook has a feature that can be added to your account, which forces you to enter an additional code that is sent to your mobile phone when you have entered valid username and password. According to the article though, this 2-factor authentication can be circumvented easily – by design from Facebook.
Yes, the article does have a point. But, they have also missed clarifying something. In one of the pictures, it states that “Because you enabled login approvals less than one week ago, you have the option to log in without entering a security code. Doing so will automatically turn off login approvals on your account”.
So, in order to minimize the number of support cases that could possibly be caused by this feature, a user that enters valid credentials and that opted-in on this feature less than a week ago has the opportunity to disable it without entering the security code that has been sent to the mobile. After that time period, the feature works exactly as anticipated and cannot be disabled without first logging on with your credentials and a security code:

These are the only options available. Also, while doing this – Facebook was opened from an “Recognized device” and immediately when the correct credentials was entered, the following notification appeared:

So, in short. Yes – in the idyllic world, this is not the preferred method, but remember – this is a feature that is not enabled by default and will work as anticipated after a week. If this feature is enabled in the belief that the credentials has been compromised, the right thing to do would be to change the username and password instead.