Buel, James William (1880). The Life and Marvelous Adventures of Wild Bill the Scout is the source for the four man fight, and it was in Jefferson County, Nebraska.
Now such sources are often embellished, BUT sometimes not so much, for you will note he didn't kill all four, and the normal human trait is to embellish toward the dramatic, thus why not simply write that Wild Bill shot all four in the head, dead?
LD
I am sure authors have help the story along but the fact still remains, he was a true gunfighter and kill more men than most. Earp try to settle things first with his fists, but Bill went for his guns first.