For the last 20 years, if you were in the bar business and knew one thing about the bartender Adam Seger, it was that he was the man behind the Seelbach cocktail.

The Seelbach is named after the Seelbach Hotel (today the Seelbach Hilton), a storied century-old lodging in downtown Louisville, Ky., that is mentioned briefly in “The Great Gatsby.” Shortly after being put in charge of the hotel’s bar and restaurant operations in 1995, Mr. Seger declared that he had discovered a recipe for a pre-Prohibition cocktail that was once the hotel’s signature drink. He tested it, liked it and put it on the menu.

The news media soon picked up on the tale, and within a few years, the Seelbach cocktail was regarded as a rescued classic. It’s a tantalizing back story, one that has charmed cocktail writers and aficionados for years, and there’s only one thing wrong with it: None of it is true.