Not until lurid headlines damned Carter Page as a traitor to his country in September 2016, six weeks before the presidential election, did he realize someone was using him to play a dirty political trick. Reporters had been hounding the energy investor with strangely detailed questions about his ties to Russia. Page told each of them that he was a former US Navy lieutenant, a graduate of Annapolis, an Eagle Scout — hardly a likely protagonist in some cloak-and-dagger drama. But he had also served as a foreign policy adviser to Donald J. Trump. And secretly, within a collection of...