What happened to Jack Twist at the end of Brokeback Mountain?

I don't think there's any doubt that he was actually killed as a result of a hate crime. As to whether or not Lureen was aware of the truth of the matter, Anne Hathaway commented on this in an interview on NPR a couple of years ago (from here):

In a November 2010 interview on the National Public Radio program "Fresh Air," Anne Hathaway told interviewer Terry Gross that she actually has no idea whether or not her character, Lureen, tells the truth in the phone conversation in which Lureen tells Ennis how Jack died. Hathaway said that she shot two takes of the scene: one in which Lureen "knew what was going on with Jake's character Jack and that he'd been cheating on me with men and that I knew about the gay bashing," and one in which Lureen "had no idea... you know, it was a terrible accident with a car tire." Hathaway told Gross that instead of using all of either take, there were shots from both takes edited into the final movie, so she doesn't know what the director's or the editor's intentions for her character or for the truth about Jack's death really were. She also said that she has never asked director Ang Lee what he thinks the truth is because "Ang knows the truth in his head, and it's not important to me. I actually think I get to be a part of the film as an audience member because I don't know, because I think the ambiguity is what is the strength of that scene and what's heartbreaking about it."

Jack Twist's death was apparently listed as an accident by the original author because that is what Lureen was having to tell people. Lureen knew that Jack was gay. She says to the other woman at dinner that her husband never wanted to "dance" either meaning that he was not interested in her sexually. Lureen knew Jack was seeing a man named Ennis regularly. She also knew he would go out to meet other men for sex. She said to Ennis that she had told Jack not to "drink" (commit the act of homosexual sex). She says Jack "drank" often. She had tears in her eyes as she said these words.

She connected with Ennis in that moment because she knew this Ennis guy and Jack were wanting to be together but couldn't. She felt the same as Ennis: they each loved Jack but couldn't have him fully. Jack cheated on them both (with other men). They were each sad that Jack had died but also angry with him for cheating because he did not heed their warnings that being openly gay would get him killed. Obviously, Ennis was devastatingly saddened at perceptively knowing how Jack truly died. Lureen had to concoct a lie because of it. She told the lie to Ennis as she had stated it many times before to others, but she knew Ennis understood what had truly happened to Jack. He was brutally beaten to death.

Edit: I keep thinking this over! My first thought was that Jack committed suicide. But, after reading other people's theories, suicide didn't seem to fit. Second thought was that he was beaten to death. Could be. Could still be suicide. I don't think it is so important how Jack died but that he and Ennis never could find fulfillment.

Personally, I believe Lureen tells the truth and the oddness and shock of Jack's death causes Ennis to imagine a possible murder and the circumstances that might be involved.