Poverty does not lead to terrorism. However, poverty leads to despair, and despair is a condition that the bad guys know how to exploit.I'm not sure Green entirely acknowledges the facts of the foreign aid game when he says things like, "we're not asking for anything other than for you to take on your own problems." Certainly many programs -- such as the Peace Corps -- largely work that way. But plenty of aid comes with very real strings: democratize, open your markets, allow military bases on your soil.
Foreign aid -- such as we've been giving lately to Haiti -- can be a powerful force for good in the world. And Green is right that, when offered with no strings, it can be a powerful argument for America abroad. But most people are going to be looking at what foreign aid buys us, and expecting results from it. That expectation necessarily lead toward some sort of quid-pro-quo on aid lending: we obviously are not throwing tremendous amounts of no-strings-attached cash at North Korea, for example. Even our spending in Afghanistan, where one would expect, based on Green's argument, to have quite a lot of no-strings aid, it doesn't really exist. Our aid is largely offered through the military, and is directed much more at trying to buy off towns or insurgents than at the basic sorts of Peace Corps/ development work that really does need to be done.
I'd love to see the basic calculus of aid change, and I think Green is right if he argues that it should change, but it's a delicate proposition at best, and unlikely in the near future.