Since when have Heads of Training been given the right to make laws? He can specify a Company requirement for the hire of the aircraft, nothing more than that. It certainly isn't a legal requirement.
Among other things it is a legal requirement for the flight to be insured.
To be insured the PIC must comply with the directions of the aircraft owner / operator - in this case a school.
If the Head of Training of that school says do not fly the aircraft as PIC from the right seat with passengers then to do so would be illegal since such actions would make the flight uninsured.
So if the Aircraft owner (or their designated representative) says you have to fly PIC from the left then the law requires you to do so or find some other aircraft operator to get you aircraft from.