That's just part of the reason, another part is the way a mobile system works, the capacitance changes in relation to the earth while driving, and so does the antenna system change with this hence changes on the meter.
That's a good point about the capacitance changing while a vehicle is rolling, which is independent of the stinger length.
Nope, it isn't the movement of the antenna itself, it is the relationship between the truck/car and the earth. There is no consistent place on earth that gives the same capacitance, even a few feet will change the earth and change the capacitance. Now when you are moving, this for some reason changes on an average and is reflected on you meter. But when it is stationary there is no movement.
Part of the loss can also be due to the flexing and moving that the antenna does in the wind. I know that when I tie the top of my antenna back in order to get into a low-ceiling parking garage, the SWR increases by a few decimal points. This makes sense to me, as the top part of the antenna is now looking at the top of the vehicle. I can see that effect on my meter every time I do it.