It was 6:30 a.m. at the United States Military Academy, the sun was rising over the Hudson River, and Paula Broadwell was in athletic gear. With a half-dozen women, she rotated between sprints and burpees. Sweating onto the pavement, the group was perched atop an overlook called Trophy Point, in the shadow of a 46-foot battle monument memorializing those killed in the Civil War. There is a female statue in bronze at the top, arms outstretched regally, who is said to represent “fame.” Ms. Broadwell was here in April for a 40th anniversary celebration for the academy’s first class of...