If that were the case, one would expect that the trackball only would be as accurate as the controller and less accurate than the mouse. However, my anecdotal experience is that the trackball is as accurate, if not more so, than the mouse, despite only using the thumb.
My suspicion is that the difference is more of a calculus problem. Moving my thumb on the trackball by a given amount changes my position by a proportional amount. On the other hand, for most games, moving my thumb on the stick by a given amount changes my velocity by a proportional amount. To put it differently, if I'm aimed at a stationary target with my trackball, I remain aimed until as long as I don't move my thumb. With a stick, if I'm aimed at a stationary target and don't move my thumb, I'll keep turning at a constant rate.
My suspicion is that the difference is more of a calculus problem. Moving my thumb on the trackball by a given amount changes my position by a proportional amount. On the other hand, for most games, moving my thumb on the stick by a given amount changes my velocity by a proportional amount. To put it differently, if I'm aimed at a stationary target with my trackball, I remain aimed until as long as I don't move my thumb. With a stick, if I'm aimed at a stationary target and don't move my thumb, I'll keep turning at a constant rate.