But what if it is not a Doomsday machine. What if it is something that can give you first strike capability while also destroying any enemy attempt at retaliation. In that case, it might make sense to keep it close to the vest, lest you destabilize MAD.
One group of aliens uses a craft the exact shape of a trashcan lid. They said this is no accident, it looks precisely the way it should look. There are pictures of it but I wont bother :)