“I’m Pat Fucking Tillman!” were the last words of Pat Tillman, a professional football player who gave up his career in 2002 to become an Army Ranger. It was also the original title of director Amir Bar-Lev’s simmering, furious “The Tillman Story,” a documentary that unravels the military and government cover-up of his death at age 27 by friendly fire near a mountainous pass in Afghanistan. Coinciding with the fakery of the circumstances of the capture and release of Jessica Lynch, Tillman’s death was used to celebrate virtues that the headstrong, freethinking man would never have endorsed. He never publicly explained his choice to leave football and fight, and this agnostic’s intellectual curiosity ranged from religious teachings of other faiths to Noam Chomsky. Was he a hero? Or a victim of an attempt to exploit his death in support of the wars in Afghanistan and Iraq? His mother, Dannie Tillman, instilled those values in Pat, and her quest to get the government to tell the truth about his death is the emotional center of a keenly observed and subtly structured documentary. (Co-editor-co-writer Joe Bini’s work includes “Wanted And Desired,” Marina Zenovich’s Roman Polanski film.) The memories of his fellow soldiers are often searing, and related in profane terms. Perhaps most infuriating are the layers of deceit in the cover-up of Tillman’s death that Bar-Lev peels away. An emotionally devastating portrait of moral men and women pitted against their own government’s lies, “The Tillman Story” is both fascinating and infuriating. Narrated by Josh Brolin. 94m. (Ray Pride)