Arm out the Window said it all really, fluids will tend to follow their straight line, the body cannot and is held in place by centripetal force, same principle as the merry go round with a floor that drops away, centripetal force holds you from dropping down.
The helium baloon experiment works well in a car. tie the balloon to the back seat, when the car accelerates, the balloon moves forward as it moves toward areas of less pressure.
Lu, you are getting worked up over nothing, an "apparent force" does not make it a force. Just accept the fact that some terms are used in place of the correct scientific or engineering term. If a rotor blade breaks off in flight, it will travel in its straight line tangental to its circular path, its just that centripetal force stopping working and thats why it let go. No big deal, no big secret, just terminology.