“Shut Up & Sing” makes us flies on the wall as it follows the media furor. We’re backstage with their manager, Simon Renshaw (“It’ll be over in three days, tops,” he predicts). We’re in the conference room with the damage-control rep sent by their “very concerned” sponsor Lipton Tea. We’re with their families as band members Emily Robison and her sister, Martie Maguire, raise their kids, compose their music, deal with the bans by Cumulus Media and Clear Channel that keep them off hundreds of country-music stations. In the midst of death threats and canceled concert dates, they forge on, creating their rousingly defiant album “Taking the Long Way” with producer Rick Rubin. Masterfully edited, the film combines footage the band made for its Web site and footage shot by Kopple and Peck over the last two years. The filmmakers are clearly in awe of the Chicks’ fighting spirit. If you think Maines’s original Bush remark was disrespectful, wait till you hear what she calls him here. Maines is not ready to make nice, and neither is this riveting documentary.