Centrifugal acceleration does not exist is one such thing. Like most questions in physics, the choice of perspective dramatically alterls the outcome. Under the normal argument, if an object rotates in a fixed axis, the linear velocity is tangential to the orbit. The object accelerates towards the center and is opposed by a normal force. If you construct the same scenario in a non fixed axis, centrifugal acceleration reveals itself.
In the end, it is the same force - and it accomplishes the same thing. You just get a slightly different picture depending on perspective.