Suggest some additional explanation be added to the Facebook integration page. All it says now is "Post updates from Facebook Pages to your group."
Should add some items such as:
Note: this integration only supports a public Page, not a Facebook group. Verify that the Page can be viewed without logging into Facebook.
The Page is polled hourly for updates. (or whatever the mechanism is so you know how long to wait to see if it's working)
Probably some other notes would be useful too.