For the many millions of us who love Paul Simon’s 26-year-old album “Graceland,” a cloud has long hung over that enterprise. Did Simon, who traveled to South Africa in 1985 for many of the recording sessions in violation of a United Nations cultural boycott, set back the cause of anti-apartheid activism? The new Joe Berlinger documentary “Under African Skies” examines these questions without much undue favoritism. (It plays for one week in Los Angeles and New York before being televised on A&E starting May 25.) The result is doubly satisfying: We get not only a trenchant political drama but a bang-up concert film as well. Although African music from the beginning was the touchstone of much American rock and pop, Simon’s fusion of American and South African rhythms was something new on the musical landscape. His “Graceland” album, which contained no overt political messages, was nevertheless seen as a political act. As he explains in the film, Simon saw himself as an artist who transcended political restraining orders. His anti-apartheid opponents, especially the African National Congress and the Artists Against Apartheid, castigated Simon for what at best they termed his naiveté. Although Simon gave credit and compensation to the South African artists, and made overnight stars of groups like Ladysmith Black Mambazo, he was still perceived as a white man freeloading South Africa’s musical heritage for personal gain. “Under African Skies” features voluminous footage of the original recording sessions in which Simon and the South African musicians are joyously jamming with each other. Berlinger also includes lengthy follow-up rehearsal footage from Simon’s 25th anniversary concert tour in South Africa in 2011. Both in 1985 and 2011, Simon looks like anything but an exploiter in these sequences. He basks in the South Africans’ riffing and jiving. Their sheer musicality is front and center. If one wipes away the political controversy surrounding “Graceland,” what’s left is the undeniable fact that, at least in the recording studio and on stage, the races were united in the highest of spirits. But, of course, that controversy is integral to this story. Simon never officially showed any remorse for “Graceland,” but he does so at the end of “Under African Skies,” after a sit-down with his old adversary, Dali Tambo, cofounder of Artists Against Apartheid. He apologizes for any harm he might have caused the anti-apartheid cause, while Tambo, in a conciliatory gesture, admits that the album broke down barriers. They embrace, and the communion seems real. Berlinger adds many voices to the mix, including those of Paul McCartney, who talks about the long history of white co-option of black sounds; Peter Gabriel, who argues that “Graceland” showed worldwide audiences that there was more to South Africa than suffering; and Oprah Winfrey, who declares “Graceland” her favorite album and a prime reason for her involvement in South African affairs. Berlinger also loads the deck a bit in favor of Simon. He prominently features Nelson Mandela’s 1990 release from prison in such a way as to suggest that “Graceland” was one of the keys that unlocked the cell door. No matter. The world has changed since 1985 and South Africa along with it. What hasn’t changed is the extraordinary music in “Graceland,” which, more than ever, and without any apparent political content, sounds like an anthem of reconciliation.