When I interviewed The Daily Show’s Jon Stewart two years ago for a documentary I co-directed, The Muslims Are Coming!, one of the questions I posed to the talk show host was: Do you think your show has had an impact on issues? Surprisingly, Stewart responded “no.” At first, my co-director, Negin Farsad, and I thought Stewart was being unduly modest. But he was actually being sincere. Stewart went on to list issues he had railed against for years—such as media sensationalism—and noted that nothing tangible had changed despite his best efforts. But if that question were put to Stewart...