Most likely the instructor is a low timer and was taught to follow the PAPI. I have seen instructor's that cannot land on 5000'. From 16k+ I can tell you the most dangerous time not to follow PAPI is in rain with good vis. Next time say "Visually above the PAPI" or "Visually below".
Yes, those of us who do not fly an automated bus do configure ourselves to land where ever we choose. From asphalt to Eskers.....