Is “Jinan's valiant general” true?

In the novel, Guan Sheng is the leader of the Five Tiger Generals of Liangshan; Chapter 091 of "Water Margin" lists: "The Five Tiger Generals: 'Big Blade' Guan Sheng; 'Panther Head' Lin Chong; 'Fiery Thunderbolt' Qin Ming; 'Twin Whips' Huyan Zhuo; 'Twin Spears' Dong Ping." The "History of Song" does record a Guan Sheng who was a defender of Jinan, who died heroically resisting the Jin army in the early Jianyan era, but it does not record that he ever became an outlaw at Liangshan.