False. Sam first wakes up before day break because Bill is screaming like a woman at the top of his lungs. To his surprise, Sam finds Johnny sitting on Bill's chest with a very sharp knife in one hand and a chunk of poor Bill's hair in the other--ready to scalp him! Sam takes the knife away from the boy and makes him lie down again, but Bill never sleeps another wink until after that boy leaves for good. Sam wakes up next right before the sun rises because, "I remember that Red Chief had said I was to be burned at the stake at the rising of the sun."
He doesn't want to admit that he is scared of being burned at sunrise, so he gets up so he won't be startled awake like Bill was. Bill catches Sam getting up and asks him why he is getting up so soon. Sam says it is because he had a pain in his shoulder. Bill then calls him a liar and afraid because Sam knows he is scheduled to be burned at sunrise, not sunset. Bill claims that Red Chief really would burn Sam if he had a match, too.