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."