I work in the heart of Washington, DC. And, if asked by a visitor where I live, I will likely relply, "DC," as well - even though it takes me two hours by car, train, subway, and by foot to get to work.
To me, and most of her "residents", DC is much larger than the 68.25 square miles in the Federal City. It is Alexandria and Arlington, Silver Spring and Waldorf. It is Fairfax and Loudoun, Prince Georges and Montgomery.
The Dome of the Capital Building and the Obelisk of the Washington Monument seem to cast their shadows from the Blue Ridge to the mouth of the Potomac; and from Frederick to Fredericksburg.
This is where I live. This is where I work. This is what I see. Each day.