It's a stupid point really, don't worry about it. What it comes down to is I don't understand how the FAA can have a system of two people logging PIC for the same flight. Only one of you can be the commander, captain, bossman, head honcho, whatever. It's not about who does the planning or handling but who was in charge, who the buck stops with. By the sounds of it you agreed before the flight that it was you, so you're justified in logging PIC. Why their system allows him to also claim credit is beyond me.