first off, it's amusing that facebook claims they're doing something in the name of user security.
if you don't have their app, the only way to log in is either using your device's browser or in an app that uses a webview in place of the browser. a webview doesn't automagically appear.
if your app simply conducts a facebook session in a webview, i see no reason not to use your device's browser. using a pc's browser to access facebook still works. i think i read the same is true for android. if you want to start your app and have the user select "log in to facebook", you can launch the browser with an intent, and then return to your app afterwards.
let's face it; they're pretty much out of control. you're not going to get too far complaining to them that your colleague can't log in even though he has the app, and you can't log in at all, and i can log in using the same tools as you...