At episode's end the Old Ranger says the Pat Garrett's daughter Elizabeth told him the story that was just shown.
In April 1878, Billy the Kid (1859-1881) and five other men ambushed William Brady (1829-1878) and four of his deputies. In April 1881, Billy was convicted of the murder and sentenced to death; he subsequently escaped and was tracked down and killed by Pat Garrett (1850-1908).
The true story of Billy's escape: Pat was out collecting taxes, the second deputy took five prisoners to dinner, and Billy asked Deputy Bell to use the outhouse. While walking back upstairs, Billy slipped out of his handcuffs, grabbed Bell's gun, and shot him.