It's frankly, in our opinion, a bug in the Facebook Login button widget. When that setting is enabled, the Login with Facebook will not sure if both 1) the user has already approved your application and b) the user is currently logged into Facebook. So, even if the user isn't logged into your site, the button won't show if both of those apply and that setting is enabled.
We actually filed a bug report about this at the end of last year with Facebook. Facebook said it was working as intended and added a note to their Login button details page:
developers.facebook.com/docs/reference/plugins/login/
Now, it says:
Note: If show-faces=true and the user is already logged in, no login button is shown.
So, unfortunately, I'd recommend not using that setting.
Hope that helps,
Alex