Question
Is it true that the root shoots will penetrate a in-ground pool wall or cause otherwise serious damage to the pool if the tree is about ten feet away? if so, how can it do it.

Answer
This is entirely too close to the pool for this tree. It has a spread of about 30-40 feet and the roots spread about 1 1/2 times this distance. It is considered an invasive tree and will have large roots near the surface of the soil. I would remove it as soon as you can.   Here is a web link that folks describe some of the problems with this tree.

http://davesgarden.com/guides/pf/go/69622/