Im with FlyerJosh. Legally you are required to be able to do anything listed in the Private Pilot PTS, which does include weight and balance. However, being that picky is kind of a d*ck move to make. I would make you do a weight and balance however you would on a daily flight and simply see if it was accurate by checking your math the old school way. If you were close I would let it go.

But try to see it from his eyes. If you were to go out on the way home and make a smokin hole... The FAA will ask him what he covered in the BFR. If he missed somethig that could have cost you your life, he could lose his ticket. In addition, your family can litigate. So he may just be practicing excessive CYA procedures.

Just remember that it is his ticket (and maybe his whole future career) on the line. So understand if he gets thourough to protect it.