By your description, you are already doing something we don't know how to do, which is run Civ 5 without Steam at all. So, either you know a trick you have to teach us, or you are mistaken and you are actually running Steam in the background in off line mode.
Has this computer ever been on the Internet? I would suspect it was at least once when you got Civ 5 and since that time has been taken off line. If you are using your Steam account from multiple computers it is possible you took this computer off line between the time you activated Civ 5 and later bought the DLC from another computer. Your computer would know Civ 5 was legit but not the DLC. If this is the case, connect the computer up long enough to let it sync up with Steam and then take it back offline.