Is “Xiao Xuanfeng Chai Jin is a descendant of Chai Rong, Emperor Shizong of the Later Zhou, and possesses the太祖's iron certificate with a vow. Because he killed Yin Tianxi, he was forced to go to Liangshan.” true?

According to the History of Song, after Emperor Taizu of Song, Zhao Kuangyin, seized the Later Zhou regime through the Chenqiao Mutiny, he indeed granted generous treatment to the Chai royal family to show his favor. However, there is no specific official record of a descendant of the Chai family holding an 'iron certificate with a vow' that could exempt them from the death penalty. Such certificates are mostly seen in exaggerated renditions in later storytelling and novels. The official history absolutely has no clue that a descendant of the Later Zhou royal family befriended bandits and went to Liangshan. The character Chai Jin is a literary fiction satirizing the corruption of the Song legal system.