That story has been going around in some circles for years.
Let me quote from the late Lee Silva, author of Wyatt Earp: A Biography of the Legend. “The myth that Wyatt Earp used a Smith & Wesson during the 1881 shootout was perpetuated by the late Earp historian John Gilcrease, who owned an engraved Smith & Wesson American Model revolver with homemade wood grips that he claimed was the gun Wyatt used in the shootout. But two other early Wyatt Earp historians saw this Smith & Wesson when Gilcrease first bought it from descendants of the John Clum family, when the gun had original pearl grips presentation-inscribed to John Clum. This evidence establishes the gun belonged to Clum not Earp. By 1881 the American Model and its ammunition were obsolete, and it is doubtful Wyatt Earp would have trusted his life to such a gun. Based on the description by butcher Apollinar Bauer of the gun Earp used to buffalo (hit over the head) Tom McLaury on the morning of the shootout, the gun was probably a 10-inch-barrel Colt Single Action.”