Deliverance

Four Atlanta men, Lewis Medlock (Burt Reynolds), Ed Gentry (Jon Voight), Bobby Trippe (Ned Beatty) and Drew Ballinger (Ronny Cox), decide to canoe down a river in the remote northern Georgia wilderness, expecting to have fun and witness the area's unspoiled nature before the fictional Cahulawassee River valley is flooded by construction of a dam. Lewis, an experienced outdoorsman, is the leader. Ed is also a veteran of several trips but lacks Lewis' machismo. Bobby and Drew are novices. While traveling to their launch site, the men (Bobby in particular) are condescending towards the locals, who are unimpressed by the "city boys".
Traveling in pairs, the foursome's two canoes are briefly separated. The occupants of one canoe (Bobby and Ed), land briefly and encounter a pair of local men emerging from the woods, one carrying a shotgun. Ed and Bobby end up in a verbal altercation with the locals before being told they cannot leave and forced into the woods with a shotgun. Ed is tied to a tree and cut with a knife while Bobby is forced to strip at gunpoint. One of the mountain men then attacks Bobby, molesting and humiliating him, when Bobby attempts to stop the assault he has his ear twisted and is ordered to "squeal like a pig", Bobby is forced to his hands and knees over a log before being brutally raped. Ed, who remained tied to a tree, is then approached by the mountain men who intend to sexually assault him.
Hearing the commotion, Lewis sneaks up and kills the rapist with an arrow from his recurve bow; meanwhile, the other man quickly escapes into the woods. After a brief but hotheaded debate between Lewis and Drew about whether to inform the authorities, the men vote to side with Lewis' recommendation to bury the dead man's body and continue on as if nothing had happened â since Lewis tells them that they will be arrested and that they wouldn't receive a fair trial, as the local jury would be composed of the dead man's friends and relatives; likewise, Bobby doesn't want what had happened to him to be known. The four continue downriver but soon disaster strikes as the canoes reach a dangerous stretch of rapids. As Drew and Ed reach the rapids in the lead canoe, Drew shakes his head and falls into the water. It is unclear why. Later, Lewis tells the others that Drew was shot.
After Drew's fall into the river, the survivors' canoes collide on the rocks, spilling Lewis, Bobby and Ed into the river. Lewis breaks his femur and the others are washed ashore alongside him. Encouraged by the badly injured Lewis, who believes they are being stalked by the rapist's partner, Ed climbs a nearby rock face in order to dispatch the stalker using his bow while Bobby stays behind to look after Lewis. Ed reaches the top and hides out until the next morning, when the stalker appears on the top of the cliff with a rifle, looking down into the gorge where Lewis and Bobby are located. Ed clumsily shoots and manages to kill him, accidentally stabbing himself with one of his own spare arrows in the process. Ed and Bobby weigh down the body in the river to ensure it will never be found, and repeat the same with Drew's body which they encounter downriver.
Upon finally reaching the small town of Aintry, they take Lewis to the hospital. The men carefully concoct a cover story for the authorities about Drew's death and disappearance being an accident, lying about their ordeal to Sheriff Bullard in order to escape a possible double murder charge. The sheriff clearly doesn't believe them, but has no evidence to arrest them and simply tells the men never to come back. They readily agree. The trio vow to keep their story of death and survival a secret for the rest of their lives. In the final scene, Ed awakes, startled by a nightmare in which a bloated human hand rises from the lake.

Question: Does the Sheriff Bullard believe their story?
Answer: No