Is “The reason Fan Yuqi fled to the state of Yan” true?

The Records of the Grand Historian, in the Biographies of Assassins, only briefly mentions that 'the Qin general Fan Yuqi offended the King of Qin and fled to Yan.' However, the Chronicles of the Eastern Zhou Kingdoms, in chapters 103 and 104, provides a lengthy elaboration, describing how Fan Yuqi revealed the King of Qin's parentage to Lord Chang'an, Cheng Jiao, and drafted a proclamation to support Cheng Jiao's rebellion. After the defeat, he 'cut a bloody path through the enemy and headed towards the state of Yan.'