I suppose your question is refering to the way in which this brilliant short story chooses to depict the flight of fantasy of Peyton Farquhar's last few moments. The narrative style of this short story is key to this approach, and certainly the story begins with a very detached narrative style, almost like a film, that deliberately presents what is seen in the most realistic way possible. Consider for example the realistic way in which the scene is described from a very objective standpoint at the beginning of the story:
A man stood upon a railroad bridge in northern Alabama, lookign down into the swift water twenty feet below. The man's hands were behind his back, the wrists bound with a cord. A rope closely encircled his neck. It was attached to a stout cross-timber above his head, and the slack fell to the level of his knees. Some loose boards laid upon the sleepers supporting the metals of teh railway supplied a footing for him and his executioners--two private soldiers of the Federal army, directed by a sergeant who in civil life may have been a deputy sherriff.
Realism is something that is attained through the objective and precise description of the scene we are given of this man who is just about to be hung. I suppose your question refers to the way that such realism makes us logically trust the narrative account that we are being given, so when Peyton Farquhar manages to escape miraculously, we implicitly believe this account because of the realism of the narrative. It is only towards the end of the story when the description turns more and more eerie that we come to doubt the truthfulness of the narrative.