The NEC requires metallic parts within 5 ft of the pool to be bonded to the Equipotential Bonding Grid.
Your case is very interesting, as there are metallic parts, but they do not have contact with any other bonded parts or to the earth. The NEC cannot forsee all types of installations, and this is one they may not have thought of. I agree that the best way to resolve this is to talk to the AHJ who can see them and make a good field decision.