Kate Logan’s investigative documentary, “Kidnapped for Christ,”which aired July 10 on Showtime, was originally meant to be an evenhanded examination of Escuela Caribe, a Christian boarding school for troubled teens in the Dominican Republic. However, when she captures institutional abuses on camera, she was compelled to take action. As a filmmaker, she got involved in the personal struggle of David, a 17-year-old gay teen whose parents sent him to Escuela Caribe to “fix” him. Logan carries messages from the gay teen in the hopes of rescuing David and exposing his (and others’) suffering and helplessness at the school.