One evening several years ago, John Mary was up late reading a local blog when he came across a comment from a man who said he lived in Gulfport, Mississippi. The commenter had been watching his kid mow a relative’s lawn, he wrote, when a couple approached the boy and asked if he could cut their grass sometime. The commenter recognized the man. It was Senator Thad Cochran, he wrote, and the woman with him sure as hell wasn’t his wife. The gossip stuck with Mary, a 62-year-old from Hattiesburg, about 70 miles north of Gulfport. But he didn’t think...