even if the pilot receives no reward.
Seems pretty solid to me. The fact you are instructing means you are working if you get paid or not. Which actually makes sense as the whole point of the FTL schemes is to limit your flying and in theory stop fatigue. If you are flying 7 days per week and doing hours before or after your duty period your not resting. The being paid or otherwise doesn't really affect your fatigue level.
And if your not putting any "work" into instructing you shouldn't be instructing.