This year’s South by Southwest Film Festival has showcased several documentaries about successful musicians, including Tom Petty, Charli Xcx and Sparks. But you could argue that they haven’t had one about a better songwriter than “Without Getting Killed or Caught,” Tamara Saviano and Paul Whitfield’s affectionate and lyrical film about Texas-born songwriter Guy Clark, which finally premiered at SXSW last week, a year after being booked for the canceled 2020 edition of the festival.

A plainspoken poet whose first album, 1975’s “Old No. 1,” contained more classic songs than most people can muster in an entire career, Clark racked up hits for people like Jerry Jeff Walker, Ricky Skaggs, Vince Gill and the Highwaymen, but rarely showed up on the charts himself until they started measuring the Americana genre, which he pretty much epitomized. He was a songwriters’ songwriter, the mentor to many and the focal point of a...