I think you have it wrong. As far as I understand, an operation is idempotent if you can perform it any number of times consecutively (without another operation taking place), and have the resulting state be the same. So for the elevator, you can press it 1 time, or 100 times, and it will have the same result of calling the elevator to your floor, so long as no operation (ex. The elevator arriving at your floor) takes place in between button presses.
I don't agree. Idempotency in terms of REST (or equivalent) is about the effect on the receiver of the call. Pressing the button each time is definitely not idempotent, because it is a change of state of the button.
The fact that the server may choose to ignore this change in terms of the travel of the elevator is not relevant to the change of state of the button transmitted by it being pressed.
...which is weird because in the elevator example, the state isn't being modified. The effect on the receiver, to use their terminology, is always to set the button to "on" or "called" or whatever you want to name it. Hence, the elevator button example is idempotent.
Quick edit: Someone else below makes a good point - in at least one part of the world, a second button press does act as "cancel". Maybe that's the confusion here?
