I thought that the flag was initially intended to be raised upside down, but because of the Sept 11th attacks they thought it would be disrespectful for the flag to be shown upside down.
I wonder if this is really true. The film would have already been in the can and there would have had to be a last minute reshoot and re-editing of the movie.
I thought that he intentionally provoked Winters reaction by feeding him the information that they planned on flying the flag upside down, but never really was going to follow through. He wanted to push Winters to his snapping point so that he would be removed from command at The Castle.