Went through the intro again just now and I'm wondering...who the hell takes the bindings off of all the Stormcloaks? If all of them were bound from the beginning nobody would have been able to cut anyone free.

God.

No, really though maybe Ralof or Ulfric had a concealed dagger and they cut off their bindings somehow?

IDK.

If you watch the opening cutscene closely, you can see them rubbing their bindings on the carriage bench. This leads some to speculate that Ulfric at least may have escaped even without Anduin's intercession.