The Activity Log error message you see about "Only administrators, developers, etc" means administrators of your Facebook Application. They don't need to be super administrators on your website.
If you haven't already, read the
Testing Open Graph Actions
section of our configuration guide. It should hopefully help.
Basically, you need to be logged in via Facebook using an administrator of your Facebook Application. You can also use the "Roles" area in the Facebook Developers area to add other Facebook users to the Developer or Tester areas so that they can test. Once the action successfully posts, you can then submit the action to Facebook so that all Facebook users can trigger the action.
I hope that helps,
Alex