This is context scramble. Why would anyone think they'd be logged out of Facebook because they logged out of a site that uses Facebook auth? That'd be like expecting you to have to unlock your front door again because you locked your car.
Because logging in was associated with Facebook, the log out got associated as well? As you said, context scramble. I think this was the point of the author; it's a bit too easy to mix up logging in and logging in with.