The Earth is a (fairly) rigid body held together by its internal structure, and is not required to be moving at orbital velocity at every point on its surface. That is, the effect you mention exists, but it is not clear that it exactly cancels the gravitational effect. (Or equivalently, it's not obvious that the tidal effect is small.) Don't forget that the Earth's rotation is reducing your effective orbital velocity on the day-side, and increasing it on the night-side.

Now, if you have some numbers showing that the cancellation is close to exact for the specific case of the Earth, that's fine. An argument showing that it's always going to be close to exact for planet-sized bodies in orbit around stars would also be convincing.