Is “Hua Rong's archery was superb, known as Xiao Li Guang. He followed Song Jiang in the campaign against Fang La, and after grief, hanged himself at Song Jiang's grave.” true?

Hua Rong's name appears in the 'Da Song Xuanhe Yishi' (Records of the Xuanhe Era of the Great Song Dynasty), proving that he existed in the early stages of the Water Margin story's transmission. However, in orthodox historical texts such as the 'Song Shi' (History of the Song Dynasty), not only is there no record of Hua Rong serving at Qingfeng Stockade or using his divine archery skills to rescue the Liangshan army from danger multiple times, but there is also no mention of his tragic act of following the imperial army to suppress Fang La and ultimately hanging himself at Song Jiang's grave out of brotherly loyalty. The novelist greatly enriched the glorious image of Hua Rong as a handsome divine archer, making him the ultimate embodiment of loyalty and righteousness in 'Water Margin', but this is not historical fact. The original text reads: "两个大哭一场，双双悬于树上，自缢而死。"（《水浒传·第120回》）