Pardon the question, but: which headwind? For an aircraft in flight there is no such thing as a headwind (or wind from any other direction), these only apply with reference to the ground.
As I said it all depends upon how we choose to model the situation. You have chosen to use the atmosphere as the frame of reference and assumed that the atmosphere is stationary (as I said in my previous post). That's fine but it is just a model.
Now lets' use the ground as our frame of reference and assume that the ground is stationary. Now we can have a headwind and in the situation which I described above the propeller would be providing just enough thrust to prevent us from moving backwards over the ground. Now when we shut down the engine, if we maintain the pitch attitude an observer on the ground would see the aircraft move aft and down. The aft movement would be caused by the headwind. The downward movement would be caused by the reducing airspeed relative to the aircraft. This demonstrates the fact that the aircraft is "experiencing" the wind.
You may wish to argue that we must always use a stationary atmosphere as the frame of reference. But this is not helpful for navigation purposes and systems such as INS and GPS do not do so. If aircraft cannot experience crosswinds why do they drift off track instead of following their noses?
As I said earlier, this whole debate stems from the fact that we choose to use a stationary atmosphere as the frame of reference. That's fine as long as we remember that this is just a modelling choice. But it does not mean that aircraft really do not experience winds in flight. We've just used our model to add the wind speed to the inertial speed of the aircraft, and then called it all TAS.
Many aircraft have been destroyed by turbulence over the years. If the aircraft could not experience the wind, why did they get torn apart? You may wish to argue something along the lines of "Aircraft cannot experience steady state winds, but they can experience changes in wind". To test this argument consider how the aircraft would experience the change. To do this it must experience the initial steady state condition, then experience the new condition, and compare the two conditions.
If this tread really isn't simply a wind up, then I can only conclude that the instructor involved forgot that it was all just a model (probably because his instructor also forgot). The student then went away with some very confused ideas.