If you're trying to make people think there might be a Batman, announcing that the Bat Signal is just a a light that goes off at random intervals is somewhat counter-productive. Any interviewer with half a brain would have wondered, "if they had so much invested in perpetuating the myth of the Batman, why are they giving it up so easily?"
Cover story aside, why do they have a Bat Signal? Wouldn't a cell phone and a simple prearranged code in case anyone's listening be more efficient?