Although the US is perhaps better trained and equipped to handle a situation like this (as you allude to), it all went south when the hostages tried to make a run for it and the terrorists started detonating bombs and opening fire on those fleeing.
This is the worst nightmare, and unfortunately, regardless of training or expertise, a situation that is uncontrollable. In a hostage situation, not all variables can be controlled, especially when the victims begin to flee.
It is a nightmare. And you're right. Once the people decided to try to make a break, all hell broke loose, and there wasn't much anyone could do except react.