Naturalism in literature describes situations when human characters are victims, or subjected to, the dictates of their natural and social environments. These characters face things which are beyond their control.
When the story opens, Peyton Farquhar has been subjected to a hanging. This is a result of his being caught by opposing soldiers. He is thus a victim of his social environment: being in the midst of a civil war. Peyton's hands are tied and a noose is around his neck. He is guarded by two privates, a sergeant, a captain and two sentinels at each end of the bridge. This describes an environment in which escape seems impossible.
As he is about to be hanged, he experiences a profound dream sequence in which he escapes the hanging and floats downstream. This is an illusion. In terms of naturalism, we can say two things here. Within the world of the illusion, he is at the whims of nature. And some of these whims help him. He is lucky that the rope breaks and that the creek carries him away from his enemies. His hope is that he is able to swim with the current while avoiding gun shots. On the other hand, this is an illusion and the events are not real and therefore, not a correct representation of naturalism. But the manifestation of the illusion is a result of naturalism. Remember that in Naturalist literature, the characters are victims of their natural and social environments. In this case, Peyton is the victim of a hanging. But he is also duped by his own mind (a part of his natural body and consciousness). He has been duped into believing he has escaped.
We might say that Peyton's fleeting illusion of escape was his mind's way of dealing with the trauma of death by hanging. The hanging, the death, and the illusion are all the result of natural and social circumstances: all of which are beyond Peyton's control. The only one that seems within his control is the illusion. However, if it is brought upon subconsciously, a result of shock, in this traumatic situation, then it is also beyond his control.