We use the same og:app_id values for different pages, yet when we run those pages through the Facebook URL Linter, we see different values for the "Admin URL" property.
Any clues why?
Admin URL is unique for all pages and open-graph pages. Even though the administrator / owner application is the same. This Admin URL is where you can set settings for that specific page only. Try visiting that Admin URL and you will see it like a real page administration inside facebook.
You only use og:app_id for publishing stream into the open-graph page wall and other things that require administrative API action.