The lights from the television studio were blinding, and the microphone still live. Chip Skinner, then working as a consultant for the Florida Department of Transportation, had just finished a careful, scripted interview. Relaxing a little too soon, he responded offhand to a reporter’s question about what happens when a car hits a dip at high speeds. His answer—casual, unguarded—outlived the interview. “I remember that to this day,” he says. “It taught me to always make sure every...