Is “The novel fictionalizes that Hao Meng was captured alive by Zhang Fei while breaking out and handed over to Cao Cao for beheading; in official history, Hao Meng was executed by Gao Shun for rebelling against Lü Bu.” true?

In official history, it is recorded that Hao Meng betrayed Lü Bu, his subordinate Cao Xing fought with him, and then Gao Shun arrived and executed him, 'Xing cut off Meng's arm. Shun cut off Meng's head, and carried Xing on a bed to present to Bu' (from 'Records of the Three Kingdoms, Book of Wei, Biographies of Lü Bu, Zhang Miao, and Zang Hong', Pei Songzhi's annotation quoting 'Heroic Records'). However, in Chapter 19 of 'Romance of the Three Kingdoms', it is fictionalized that Hao Meng escorted an envoy to seek help from Yuan Shu, and on his return, 'Hao Meng exchanged horses for only one round, and was captured alive by Zhang Fei... Cao Cao was furious and beheaded Hao Meng at the military gate.'