The category was the same one that he and director Malik Bendjelloul picked up last night in Hollywood.
Their elusive subject was not in the audience, however. "He's genuinely a humble man, and he wanted to stay at home in Detroit watching television," said Mr Chinn.
Their film beat an Israeli film and a Palestinian film to triumph in the category.
Elsewhere, there was disappointment for Steven Spielberg, who failed to pick up his third Best Director trophy for the epic Lincoln.
But its star, Daniel Day-Lewis, whose mother was Jewish actress Jill Balcon, was named Best Actor at the ceremony, earning him his third Oscar and setting a record.
"I really don't know how any of this happened," he said in his acceptance speech. "I do know I've received much more than my fair share of good fortune in my life."
