The access and display is controlled completely by Joomla itself. Our code doesn't control what type of users can see the module.
I'm not sure why it would only display to logged in users, but I'd test all the various configurations of different access levels and make sure it's not just when you're logged in via Facebook alfeady. For instance, the page module may only be displaying to users that are members of the Page due to restrictions/privacy settings for the page.
Another test would be to enable the title of the module to see if that displays. If so, it means the module is trying to show to guests, but for some reason isnt.
Any of the above information will help us narrow things down and help get you going.
Thanks,
Alex