As Martin said, it's possible with the Graph API using FQL. I tried Martin's solution, but needed to change it a little bit.
Defining filter_key = 'others'
didn't help. Instead, you can replace it for actor_id != YOUR_PAGE_ID
, so, in the end, you can have:
https://graph.facebook.com/fql?q=SELECT post_id, created_time , app_data, type, actor_id, target_id, message FROM stream WHERE source_id = YOUR_PAGE_ID AND actor_id != YOUR_PAGE_ID&access_token=YOUR_ACCESS_TOKEN
If you need more variables, you just need to put them after SELECT, and you can check them out here: https://developers.facebook.com/docs/reference/fql/stream
On iOS, you don't need to put the access token in the query. To check how to do it with the latest iOS SDK, see my answer here: https://stackoverflow.com/a/14357179/675486