And since Obama gets all his info from our media he may well believe that he’s really not doing anything in Iraq. Or maybe, he’s not really in control any longer and doesn’t know that either because those actually running the show haven’t had a press conference yet.
The other distinct possibility is that Zero doesn't know authorizing "air operations" usually entails authorizing forward air observers and their security teams.
Or it's another NATO member trained with the US for air ops (like the Germans or Brits) fulfilling that role.