Welcome to Physics Stack Exchange. This is a good question and had me stumped for a bit. The solution is to remember that the centrifugal force is a fictitious force. It only appears to be a force when you view it in a rotating reference frame (such as the one in which the moon is stationary). When you view it in an inertial reference frame, you see that this apparent force is simply a function of the moon's inertia. Since the centrifugal force is fictitious, it doesn't count. :)