PEBBLE BEACH, Calif.—Twenty years ago, one of the most coveted pieces of golf real estate in the world was back on the market. Pebble Beach, the picturesque, seaside host of this week’s U.S. Open, was about to be sold by the Japanese company that had bought it only seven years earlier. It would be the fourth time in two decades that the iconic course changed hands.

Peter Ueberroth—former Major League Baseball commissioner, architect of the 1984 Olympics in Los Angeles and longtime Pebble Beach visitor—imagined how the ownership...