The problem is that engineers are taught about autorotation by viewing and subsequently pondering static diagrams that show a 2 dimensional airfoil with arrows emanating from it indicating L (for lift) and D (for drag) along with an accompanying description about how the resultant vector (usually described as "thrust" T) drags the airfoil around in circles - thereby resulting in autorotation.
It's not that easy to mentally segue from that static 2D textbook scenario to the very dynamic and entirely 3 dimensional situation that actually describes true autorotation. Also, if you think about autorotation in this purely bookwork context, it somewhat makes sense that the airfoil would not autorotate without forward velocity. And in actuality it won't - that is without some initial forward velocity in order to get the autorotation started first (i.e. prerotation). Remember that autorotation is a conditional phenomenon. Your gyro blades don't start spinning on their own (even with wind blowing through them) without some preliminary action to get them started in motion first. And once they're set into motion, action must be immediately taken to keep them in autorotation, which necessitates either a headwind or constant forward motion (while still on the ground). At this point, the students are correct. And in fact, up to certain non-flying rotor rpms, they remain correct.
Once in the air and the blades are well into autorotation, at that point the oncoming airflow through the rotor no longer has to come from a forward direction, it can also come from directly below (as occurs during a vertical sink). The confusion from the student's part is that the dominate forward velocity component over much of the rotor is now coming from the spinning airfoil element itself. When the student misses this critical observation, the student is missing the very essence of AUTO rotation. The blades at this point rotate by their own spinning action. They're absorbing the energy associated with the oncoming airflow from the vertical sink and converting that energy into LIFT, DRAG and rotational energy. The pitch of the blades is set at a sufficiently low (fixed) angle that the resultant airflow vector causes most of the airfoils to pull themselves around in a circle (unlike a helicopter with collective pitch which can quickly fall out of autorotative status without a rapid reduction in pitch). The rotor has transitioned from the static 2D static image on their textbook page stuck in their heads to the very real 3D (actually 4D) dynamic and self sustaining rotational status associated with true AUTO-rotation.
I would suggest telling the students that autorotation is just that; SELF sustaining rotation. And that autorotation is highly conditional. It will not happen if the rotor is stationary. It will not happen if the aircraft is flying too fast (i.e. where retreating blade stall and advancing blade compressibility halt normal autorotation). But as long as the rotor has in fact transitioned into autorotation and is flying within these conditional parameters, it WILL fly and sustain controlled flight, even in a pure vertical sink.