The example of the Earth's axis always pointing at Polaris is an excellent example indeed. The axis of the Moon's orbit (and rotation, they are tidally locked) also points in a unique direction as the Moon goes around. There are always more complicated effects-- the Earth's axis takes 26,000 years to precess in a little circle, so does not always point at Polaris but does for our lifetimes. The Moon's axis precesses much faster, because of effects very similar to what you are talking about-- the Sun tugs harder on one side of its orbit. But just as with a gyroscope, such tugs have a surprising effect on the orbit. Instead of changing the overall tilt, it just causes the axis to precess at a slightly different rate than the once a year you get from purely the coriolis effect in the co-orbiting frame. To understand this counterintuitive process more, just look up "precession" and "gyroscopes". Basically, until you actually solve the equations to find the resulting behavior, it's hard to guess in advance what will happen. This was the source of your mistake, but as I said, it is a very easy mistake to make and does not represent unintelligent reasoning, it merely shows what a lot of us have learned the hard way-- we must always be cautious until we have actually solved the equations of motion.