So if you fly cross-controlled - ie put in left pedal and right cyclic, you are travelling in a straight line but the ball is out to one side - that is steady state not acceleration.
An accelerometer that feeds into an AFCS to produce coordinated turns senses the lateral acceleration that occurs when you roll into a turn without adding pedal (skid or slip) it then feeds a signal into the yaw channel to reduce that skid (acceleration) thus giving a balanced turn. A balance ball won't do that for you which is why they wire in accelerometers and not balance balls.
With your reference points you have two rates of movement to contend with - one of the camera panning with respect to the scenery and one of the aircraft moving with respect to the scenery. Therefore two rates of angular change which are different with respect to the observer (the camera).
What magic maths did you use to eliminate the parallax error?????