In public, Donald Trump's health czar Robert F. Kennedy, Jr. has become a surprise vaccine advocate amid the growing measles outbreak. His private comments, however, betray his conspiratorial leanings.

On Sunday, Robert F. Kennedy Jr. met with the families of two girls who had died from measles in West Texas—and raised doubts about the safety of vaccines. “He said, ‘You don’t know what’s in the vaccine anymore,’” Peter Hildebrand, whose 8-year-old daughter Daisy’s funeral had been held just hours earlier, told me. “I actually asked him about it.”

Robert F. Kennedy Jr. stayed mum on a touchy topic during a dinner with the dad of an 8-year-old girl who died of measles, the man said.