John Kerry starts by showing the entry in a log he kept from 1969: "Feb 12: 0800 run to Cambodia." Graphic: Kerry's New Evidence He moves on to the photographs: his boat leaving the base at Ha Tien, Vietnam; the harbor; the mountains fading frame by frame as the boat heads north; the special operations team the boat was ferrying across the border; the men reading maps and setting off flares. "They gave me a hat," Mr. Kerry says. "I have the hat to this day," he declares, rising to pull it from his briefcase. "I have the hat." Three...