Factual error: The geographical context of the film is wrong. Riverton, Wyoming (as the name implies) is in a fertile agricultural river valley. The surrounding country is uncultivated desert. There is none of the extensive grasslands shown in the film. Moreover, even in the 1960s Riverton, which is a county seat and market center, was much more substantial than the film implies.
Factual error: The deer shot by Ennis is not an elk but a European red deer. There are no wild red deer in the USA, only imported and fenced in.
Answer: Lureen may have been lied to about how Jack died. As a kid, Ennis had seen the body of a man that was killed for being gay. Knowing that Jack was 'seeing' other men, Ennis knew that he must have been killed for that reason instead of the way that Lureen explained it. Even if she did know the truth, she may have lied to him because she didn't want Ennis to know how Jack really died.
Jane Doe