Here are the instructions for (for example) Anderson sliders; self-adhesive flashing over the house-wrap installed in the correct sequence is the method shown - no additional head or other flashings.

However note that Anderson puts the responsibility for flashing design and performance back on the architect / designer / builder / cladding manufacturer. So the inspector may have had valid reasons for calling for more rigorous measures than the generic flashing instructions supplied with the window, depending on his/her experience and or local requirements and practice.

------------

BTW, I had not read those instructions for a few years and had forgotten (if it was even in there when I last read them) the caution against installing reflective flashing under vinyl . Seems I learn (or re-learn) something new here every day...