Bill and Sam choose Summit, Alabama as a location for the kidnapping because, within the time frame of this story, the Appalachian area in northern Alabama is remote and sparsely populated. Sam also considers the people rather backward.

It contained inhabitants of as undeleterious and self-satisfied a class of peasantry as ever clustered around a Maypole.

Furthermore, the two men know that without any large city nearby, the law enforcement in this town must be minimal. 

We knew that Summit couldn’t get after us with anything stronger than constables and, maybe, some lackadaisical bloodhounds and a diatribe or two in the Weekly Farmers’ Budget.

Sam and Bill also assume that they have little to fear about any interference with the success of their plans. Because they stay about two miles away, at an elevated point where there is a cave in which to store their provisions, the men feel that they can safely keep a lookout over the town and spot any unusual activity in time to escape.

Indeed, the humor of this story lies in Bill and Sam's erroneous assumptions about the residents of Summit and their expectation that kidnapping the son of the richest man in town will be easy and profitable to them. For in the ironic reversal of O. Henry's ending, Bill and Sam are the ones who have been terrorized, not the kidnapped boy. Pretending he is Red Chief, the boy tortures his captors both physically and psychologically. Also, the wealthy "mortgage fancier and forecloser" Dorset refuses to pay the ransom, demanding, instead, that they pay him to take his son back.