“Muhammad Ali, born Cassius Clay, was not the only American to refuse to serve during the Vietnam War, but he was, by some measures, the most famous, the loudest and the baddest. Tracing the road to Mr. Ali’s act of defiance in 1967, Bill Siegel’s film ‘The Trials of Muhammad Ali’ tries to recover the cultural éclat of the moment after decades of pop-history shorthand have reduced it to sound bites about the Vietcong. Mr. Ali has already received his share of attention, not only in the annals of sports journalism but also through documentary (‘When We Were Kings’) and drama (‘Ali’ and ‘The Greatest’). But Mr. Siegel’s entry dwells on Mr. Ali’s embrace of Islam, and specifically the Nation of Islam, and how his stance on the war led him out of the ring and all the way to the Supreme Court. Sifting through the plentiful footage on…