I would say the main reason they are stored underwater is mostly because they need a place to transfer heat to lest they melt and cause a critical mass of spent fuel.
They do it for both reasons. The hydrogens in the water molecules are good at absorbing neutrons. The control rods are also typically made of carbon, and will release x-rays, which the water is also fairly good at blocking. Not as good as gold, but who's got that kind of money.