Alexie's collection of stories portrays American Indian culture in such a way that it is simultaneously a response to the centuries-long marginalization of the indigenous people by the whites and, as well, a picture of the long-term effects upon Native Americans of what has amounted to cultural (and actual) genocide. The title alludes to the popular radio and television series The Lone Ranger of the 1940s and 1950s, in which the title character is accompanied by his faithful Indian companion Tonto. The last thing that would ever have occurred on the actual series is a fistfight between these two. Tonto's devotion to the Ranger is absolute, an unfortunate symbol of the Indian's subservient position with regard to the Anglo. Though the Ranger never mistreats Tonto, and every indication is that their companionship is genuine, the white man is clearly the leader if not the master. Looked at from the perspective of what actually transpired between whites and Native peoples over the centuries, the TV show is an uncomfortable portrayal of a dysfunctional dynamic, though sugar-coated to make it look normal and benign. So in his title Alexie is overturning this stereotyping and celebration of the white man's victory and dominance over the Indian by imagining a fight between them.
This is not to say that most of his stories portray open conflict between the two groups. Alexie's focus is primarily upon his own people in situations that are microcosms often of the overall tragedy of American Indian history. At least one story in the collection, however, is especially important to discuss in the context of your question about the title. "Distances" is a brief dystopian tale in which the white culture has been destroyed in a cataclysm, a fulfillment of Wovoka's prophecy. Wovoka, the late nineteenth-century leader also known as Jack Wilson, believed that the Ghost Dance was a means by which Native Americans could enact a rebirth of their people and would restore their former glory. In Alexie's story a Tribal Council decrees that any remnant of the culture of the whites must be destroyed. Indians themselves are divided into two groups known as the Skins and the Urbans; the latter, those who had lived in the cities, are thought to carry an illness and are discriminated against by the rural Skins. Altogether, however, the story is a post-apocalyptic tale of a world in which the whites' victory over and subjugation of the Indians have been reversed.
Yet the message of this bleak dystopia shows, if anything, that vengeance against the whites unremarkably fails to achieve a solution to the fate of the American Indian. The title of Alexie's collection of stories is a metaphor of the conflict being a continuing one, ambiguous in meaning like so much in history and in the human imaginings of the future. No one can say which of the two will win this fistfight, and the implication is that both are losers in the long run.