Is “The circumstances of Gongsun Zan's defeat and death.” true?

In the novel, through Zhao Yun's words, it is said that Gongsun Zan, because he did not listen to others' advice, 'was defeated and burned himself to death' (Romance of the Three Kingdoms, chapter 28: 'Unexpectedly, Gongsun Zan did not listen to others' advice, leading to his defeat and self-immolation.'). In the official history, it is recorded that he indeed died knowing he was doomed, but the details are that he killed his wife and children before hanging himself, rather than simply burning himself (Records of the Three Kingdoms, Book of Wei, Biographies of the Two Gongsuns, Tao, and the Four Regional Lords: 'Zan, knowing he was doomed, killed his wife and children, then hanged himself.').