Ahhh.. we think we know what the issue is. Is the Facebook user that is trying to authenticate an admin, developer or tester of the Facebook Application? If not, you'll need to go to the Facebook Developer Area, click into your App and go to the Status and Review section. In there, click the "Start a Submission" button. Then, in the popup, select the following permissions to have them allowed by your app:
publish_actions
user_groups
Those will need to be reviewed and approved by Facebook for your app to use them.
For Facebook users that are admins or developers of your app, you don't need to go through the approval process. For all other 'normal' users, you have to have Facebook approve the permissions before they can be used.
I hope that helps, but if not, let me know.
Thanks,
Alex