When Clay T. (Tom) Whitehead arrived at the Old Executive Office Building on August 7, 1974, dressed as a cowboy, he surely didn’t want to run into Henry Kissinger. Whitehead was supposed to be on vacation in the Rockies, but a last-minute emergency meant he had to stay in D.C. “Well, you know, I got tied up for a little while,” he explained to President Richard Nixon’s powerful National Security Advisor. Kissinger, ever paranoid about being out of the loop, protested: “What is going on here? Something is going on here.” What was going on had started three months earlier...