Despite a PR and marketing blitz that had Oliver Stone on a whirlwind tour of Latin America, his latest documentary “South of the Border” has sunk like a rock at the Venezuelan box office.Local observers in Venezuela have reported empty cinemas, indicating a stunning indifference to Stone’s pic, a documentary about South American leaders that devotes a hefty amount of screen time to the country’s President Hugo Chavez. In the 12 days after its June 4 debut, it grossed only $18,601 on 20 screens, according to Global Rentrak. Showings on mobile screens in rural areas (where Chavez has more popular support) have attracted crowds, but these screenings are free. The doc’s Venezuelan distrib, Raul Chamorro’s 9 1/2 Communications, reports that some 1,300 people came to the mobile cinema screenings in the towns of Vargas and Guarico. In the pic’s defense, Chamorro says documentaries don’t tend to do well in Venezuela. “We were hoping that Chavez would call for people to see it, but he hasn’t,” says Chamorro. “It has been a disappointment.” The highest-grossing docu in Venezuela is Michael Jackson’s “This Is It,” which earned $2.1 million. “Border” fared a bit better in Argentina, where it grossed $41,095 on 16 screens in the 14 days since its June 3 debut. Brazilian distrib Europa Filmes reports a cume of $21,385 from 11 screens as of June 17. Stone has had better luck in the region with his fictional works. His top-grossing pic in Venezuela is “World Trade Center” with $447,364. In Argentina, “Alexander” made close to a million dollars. Buenos Aires-based Pampa Films is rolling out “Border” across other territories in the upcoming weeks.