Their society and culture is informed primarily by their religion.
"In a documentary a few years ago that was made in Indonesia, many Muslims were interviewed and most were moderate in their beliefs, much like anywhere else."
Here's a map showing the various interpretations of Sharia law in different countries.
As you can see it is heavily dependent on the location, there are far fewer Shia in Indonesia.
"So, when we prove them right by invading and torturing Muslims, we shouldn't be surprised if some of the less stable people, and more vulnerable turn to extremists for protection."
Only if they conclude that the actions taken, torture in this case, justifies revenge(joining an extremist group). And their law(their religious scripture) enforces an eye for an eye mentality. Taking action with a plot for revenge ignores the fact that the logical progression that is justifying their actions to them, may be the same as the one used to justify to others the actions they themselves are seeking to avenge. Leaving them in a hypocritical, self destructive cycle, enforced by religious law. When in reality no actions from either party was justified. We shouldn't be surprised that a number of them turn to extremism as a reaction to anything they find to be justifiable with violence via their unquestionable scripture. Which includes many things, from drawing pictures of Mohammad, to adultery or leaving their religion. Their acceptance of the claim that said revenge is justified is on their heads. I don't find the original reaction to 9/11 by torturing for information to be justified either.
"She was particularly worried about her young son who, she said, was very upset over the Iraq war and the anti-Muslim rhetoric coming from the west."
Not all anti-muslim rhetoric is bigoted, but that's what that statement suggest. There are very good arguments to be made against Islam regarding its divisiveness, inability to evolve with society, factual incorrectness, etc, all with a logical basis. And Islam, not to mention all the Abrahamic faiths, have had a record of becoming angry and violent in reaction to criticism of their beliefs. That kind of religiously based bullying and censorship can't be allowed. They can be upset all the want with people criticizing their religion, the problem is when they take a step towards violence through frustration with their inability to defend their position in the arena of words, and that's what we are seeing.