Is “In the 'History of Song·Biographies of Confucian Scholars', when recording Sun Shi's service as a lecturer to Emperor Renzong of Song, the text mistakenly wrote Sun Shi as Xing Bing, the subject of the preceding biography.” true?

In the 'History of Song·Biographies of Confucian Scholars 1', the biography of Sun Shi records his deeds after Emperor Renzong ascended the throne, when he served as a Hanlin lecturer: 'When Emperor Renzong ascended the throne, the chief councilor requested that a renowned Confucian scholar be selected to lecture on the classics, so he was summoned to be a Hanlin lecturer... Whenever he lectured on the chaotic rulers and fallen states of previous dynasties, he would repeatedly admonish and remonstrate. If Emperor Renzong's attention wandered, Bing would stand silently and wait, and the emperor would then become solemn and change his attitude.' The text here records Sun Shi's deeds, and moreover, Xing Bing, the subject of the preceding biography, had already died in the third year of Dazhong Xiangfu under Emperor Zhenzong, making it impossible for him to serve as a lecturer during Renzong's reign. Clearly, this is an error where the historian or copyist mistakenly wrote 'Shi' as 'Bing'.