When the grandson of the richest man in the world was kidnapped by Italian gangsters in the ’70s, his grandfather refused to pay the ransom until he received the teenager’s severed ear in an envelope. Even then, J. Paul Getty haggled with the captors until the price for his grandson’s release was suitably tax deductible.

The incident, just one of the Getty dynasty’s many family misfortunes, is depicted in Ridley Scott’s new thriller All the Money in the World. At the time, John Paul Getty III’s abduction made headlines around the globe, and the trauma...