I grew up in Arlington, only moved away quite recently, and have also never heard anyone use the expression reppin the DMV. Also, I would argue that there are pretty considerable differences between the constituent parts of the metro area. Even Arlington and Fairfax are fairly dissimilar. Still, I think people who live in contrasting areas like Bladensburg or Alexandria still have an idea of what the area as a whole is like.
I also find it weird that a lot of people say DC is a dirty or a boring city. Honestly, as stupid as it sounds, I think people think it's not exciting because it doesn't have any skyscrapers. I guess there isn't as unified of an entertainment district as in some other cities.