Bradley Cohen, a wealthy Los Angeles real-estate investor, was enjoying a vacation dinner with his wife on the shores of Italy’s Lake Como when a Google alert flashed on his phone.

The alert linked to a website carrying the headline: “Is Bradley S. Cohen the Next Bernie Madoff?” It showed a photo of Mr. Cohen alongside a photo of the notorious swindler with a list of allegedly “alarming similarities” between the two men. It falsely suggested Mr. Cohen had criminal convictions for fraud and money-laundering and that his industrial...