No, that's not the reason. I am aware that you are talking about the coriolis force from the orbit about the Sun, that's what I'm talking about too. And I'm telling you that if you exert forces on a gyroscope, or a spinning bicycle wheel, the response of the spinning object may surprise you. In this case, the spinning object is the Moon orbiting the Earth, and when the coriolis force from the orbit about the Sun acts on that system, it does not produce the effect you describe, it produces the effect I described. That's just what happens, either solve the equations or simply note that the coriolis force conserves the orbital angular momentum of the Earth-Moon system when you transform back to the reference frame where the Earth is in motion.