iOS Facebook app stuck in logged in state - how to log that user out?
When I still had the profile pics (or, rather, the one that I wasn't able to delete from the Setup app) visible in the Facebook app, I noticed that there was a link at the bottom of the screen called 'Login Settings' or something along those lines. Tapping that brought up a dialogue that lists the accounts that are set for instant login, so I was able to delete the other account from there (you can set or change passcodes from there, too, if that's your preference), and I'm back to the more secure old behaviour of needing to type in the passwords for all of our accounts.