Dr. Mark Hyman didn’t hesitate before accepting an invitation, 14 years ago, to a weeklong white-water rafting trip with Robert F. Kennedy Jr.

Mr. Kennedy, the environmental lawyer, conspiracy theorist and political scion, was bringing like-minded souls to the wild, undammed Futaleufú River in southern Chile to raise awareness about a hydropower project threatening the valley. Dr. Hyman was exactly the type of expert Mr. Kennedy forged alliances with: a doctor who bucked the mainstream and had a roster of well-heeled clients.

At one point on the trip, Dr. Hyman recalled, his raft overturned, and he clung to it until the group reached calmer waters. Later, on shore, he and Mr. Kennedy indulged in a gaucho-style barbecue. “It’s a dangerous river,” Dr. Hyman said in a recent interview with The New York Times. “We survived that experience together.”

The two men have bonded on many other getaways in the years since, often discussing Dr. Hyman’s preventative approach to health care, known as functional medicine. As their connection grew, so did their fame.

Dr. Hyman, 65, has amassed millions of followers interested in his booming wellness empire, which includes a supplement company, a hit podcast, 15 best-selling books and a start-up health testing company with celebrity backing.

And the doctor’s adventure partner, Mr. Kennedy, ascended to become an independent presidential candidate and, now, President-elect Donald Trump’s pick for the next secretary of Health and Human Services, vowing to “Make America Healthy Again.”