Last October, embarrassing e-mails leaked from New York City’s Department of Health and Mental Hygiene disclosed that officials had stretched the limits of credible science in approving a 2009 antiobesity ad, which depicted a stream of soda pop transforming into human fat as it left the bottle. “The idea of a sugary drink becoming fat is absurd,” a scientific advisor warned the department in one of the e-mails, a view echoed by other experts whom the city consulted. Nevertheless, Gotham’s health commissioner, Thomas Farley, saw the ad as an effective way to scare people into losing weight, whatever its scientific...