This is absolutely correct, your duty station is DC and therefore you get DC locality pay (I heard that was actually the reason for it, because they know academy basic pay is so shit). You're just on TDY to the Mike Monroney Aeronautical Center.
It makes for an interesting time the following April, because you were never actually a DC resident and therefore you don't owe the DC taxes they took out, you actually owe them to the state you lived in before going to the academy. You have to submit a form to DC to get those taxes back.