Is “The biographical arrangement and evaluation of Han Xin, King of Han, who surrendered to the Xiongnu, in official histories.” true?

In the Records of the Grand Historian, 'The Biographies of Han Xin and Lu Wan,' Han Xin, King of Han, is grouped with Lu Wan, lamenting that they rose by deceit and force and ended in distress, fleeing to the Xiongnu: 'Han Xin and Lu Wan were not of a generation that accumulated virtue and goodness; they seized momentary changes and succeeded through deceit and force. Encountering the early stability of the Han, they were able to obtain territories and face south as lords. Internally suspected by the powerful, externally relying on the barbarians for support, they thus became increasingly estranged and endangered. When their affairs were exhausted and their wisdom was strained, they finally fled to the Xiongnu. Was it not pitiful!' In the History of Han, 'The Biographies of Wei Bao, Tian Dan, and Han Xin,' he is instead grouped with Wei Bao and Tian Dan, viewing him as a descendant of the old nobility of the Six Kingdoms: 'During the conflict between Chu and Han, heroes became kings; only Wei Bao, Han Xin, and the Tian Dan brothers were descendants of the old states, but they were all cut off in their own lifetimes.'