What he is being told that if he gets this bbp to sbp adapter, the rim will not fit..says the center hole in the middle is too small.. 2 inch vs 3 inch..
Your thinking is correct as long as there is room for the studs that are in the adapter to clear the bbp hub.
The sbp wheels do have a smaller hole than the bbp does but as you said the hub on the bbp is tapered. I would have him take off one of his wheel and slide yours up to his studs so he can see the clearance.