“Yoko Ono: ‘I Had An Affair With Hillary Clinton In The ’70s,’” read the headline in World News Daily Report, a website that peddles made-up stories.

Next to the story? An ad for the 2017 Ram 1500 truck, made by Fiat Chrysler Automobiles NV.

Big brands, often inadvertently, are helping fund the websites at the center of a growing controversy...