So the army flag was backward?
It was proper. If it was on the players left shoulder it would look ‘normal’. When it is on the players right shoulder it would look ‘backward’ but that is correct. It is ‘backward’ so that the blue part faces the direction you are walking. This is true on regular soldier uniforms as well.
Think of it like a flag on the back of a motorcycle blowing in the wind. No matter which side you look at the moving motorcycle, the blue part (union) is always facing forward. :)