Believing the opposite of what is true is a trap into which both the protagonist of this story and the audience falls. Peyton Farquhar desperately wants to help in the war against the North. He is so eager to be involved, in fact, that when a man in a Confederate uniform comes by the house, Peyton doesn't question the man's credentials. He blindly accepts that this man is loyal to the South, and he blindly accepts the story that the Owl Creek Bridge needed to be destroyed to stop the advance of the Union army.
Peyton also his perception to deceive him. He goes off to take care of the bridge, and is easily caught by the Union soldiers - it was their soldier in disguise that trapped Peyton with the fake story. Peyton is to be hung for trying to destroy the bridge.
This is when the readers are tricked by perception. Peyton's final thoughts revolve around a possibility for escape. He imagines that the rope breaks, that he is plunged into the river and swept downstream. He imagines avoiding the gunshots and travelling all day to return home. The narrative is written to make this section seem real - the audience has no way of knowing that it is all in Peyton's imagination until the last moments of the story. The audience's knowledge of what is happening to Peyton has been tainted by this narrative. It isn't until this line - "Peyton Fahrquhar is dead" - that readers know the truth.