There was a peculiar moment during a news segment last fall, at the height of the Ebola scare in the United States, between the nation’s two most recognizable medical figures. Sanjay Gupta, CNN’s household-name medical correspondent, was standing next to Thomas Frieden, the director of the Centers for Disease Control and Prevention, in front of CDC headquarters in Atlanta on October 1. Frieden assures Gupta that if one of them had Ebola, the other would be at no risk of infection: “It’s not like the flu, not like the common cold. It requires direct physical contact.” A CNN anchor interjects:...