Are you referring to sidewall bulge making it more prone to direct damage? While that may also be true, it's not what I was referring to!
Lowering the tyre pressure increases the amount the tyre deflects under load (due to the car itself and/or any road imperfections). As the tyre deflects more, it becomes more likely that the fragile sidewall/shoulder of the tyre will come in contact with the road surface and/or any debris on it.
Here's a visualization: http://automotive.kendatire.com/medi...pad&width=1200