Yes, I believe "free will" is the key, although God already knows, and always has known, all the choices we'd make.
When one considers "natural disasters," I'm glad someone pointed out that much could have been done to prevent countless lost lives. Instead of "where was God?", perhaps the question should be, "where was Man?"
Why didn't Man do what he could to prevent all the lost lives? Greed, probably.
What about the baby born addicted to crack, or with AIDS? Where was God? Where was Man? What choices did Man make to create a child with such problems? How many diseases could be cured and/or eliminated if it weren't for greed, lust, amoral or immoral behavior?
Also, another thing: When a natural disaster strikes, and many people die, somehow we all assume they were "innocent" people. We do not know that they were. May be safe to say the children were "innocent" relatively, but certainly not all the adults were "innocent" even in our eyes, let alone God's eyes.