When I first noticed this, I assumed that I was making some sort of mistake. In the video for "16 Military Wives," we learn about the majority of characters through their Model United Nations affliations. As you can see from the picture on the right, one of the United States' three friends is the Republic of Korea.
However, in an earlier scene in the video, we see the school's Model United Nations in action. Take a look of "Korea's" flag, which is that of the Democratic People's Republic of Korea.
I have not been able to decide whether this is a mistake, or clever commentary on the Bush Administration's handling (or rather, mishandling) of North Korea.