"Another resolution for this would be for America to bow to the demands of a small group out of fear. If this happens, does anyone actualy expect this small group to stop making demands?"
I believe that everyone, this small group included, understands that any bowing on America's behalf is an action of sane respect, not fear. But since America has been and remains reluctant to give in to any demands whatsoever (on foreign territory I might add), what other means than violence do they have left?
You might also want to take a look in the mirror before patting yourself on the back over your supremacy, for your reactions are no better than their actions.