At a time when the stories behind shocking headlines are routinely turned into true crime podcasts and star-studded Netflix series, the question of how to tell them ethically is often raised. For its part, Mike Ott’s McVeigh delivers about as un-exploitative and un-sensationalized a depiction of Oklahoma bomber Timothy McVeigh as could possibly be imagined—to the point that, if anything, the film ends up understated to a fault.

McVeigh begins with Timothy (Alfie Allen) driving down a country road as weathered as his car. Nothing happens for a spell, until Timothy is pulled over by a cop. But nothing much happens at this point either, and Timothy is soon free to continue on his way. Something about the relative lack of incident and the dreary, sparse environment puts us on edge. From the start, McVeigh thrums with a sense of alienation and hostility so pronounced that even those...