I think it really depends on the water table that exists where you live. Those trees that are planted in a water table that is close to the ground will tend to move the roots out rather than down, especially if they are intolerant of having "wet feet" so to speak. Oak trees come to mind in that regard.

Those that are tolerant of water like weeping willows and cypress need to have water close by.

Check from your local county extension office with the horticultural agent, and they will advise you for what is best beside a pool.

Hope this helps.

Pat