Assuming Berg and the murderous thugs sort of knew each other, what if Nick 'posed' for the video, thinking it was a PR type stunt. Notice in the video that he does not show much reaction while sitting on the floor, as if he doesn't know what is about to happen. Nick cooperates in filming the PR stunt, but at the last moments, Zarqawi and company perform the real act.
Imagine he is friendly with some bad guys, they find he's been interviewed by Iraqi Police, and the FBI while being detained, he's released and........