I think that the concepts of bonding and grounding are being confused here. Bonding would prevent a difference in potential between the various gear that is bonded together (pump, light, pool, ladder etc). There should also be at least one earth ground on the bonding line. It sounds to me like there is really a difference of potential between the ground its-self and the bonded pool gear. Possibly because the earth ground for the bonding setup was sunk near the pool pump equipment and there is a difference in potential between that location in the earth and the location where this person's pool deck is at. I'm not sure if it's really possible to bond concrete, is it? It might be worthwhile to sink another deep earth ground to the bonding line near the pool and/or decking to try and solve this particular problem. Or it could certainly be a faulty bonding line like Pooldoc said in the first place.

Another thought I had was that if the setup has any significant age, the ground rod could have simply corroded enough that it's no longer serving it's purpose.