In 2004, a judge gave permission for the Barnes Foundation, with its unparallelled collection of Impressionist, Post-Impressionist and Early Modern paintings by Renoir, Cézanne, Matisse and others, to relocate its gallery from suburban Merion, Pa., to downtown Philadelphia. More than a decade of brawling—in the courts, the streets and the media—over the foundation's purpose and priorities, has ensued. A new documentary, "The Art of the Steal," directed by Don Argott, skillfully summarizes much of this history...