Is “The biographical style of Lu Wan and the lament over his defection to the Xiongnu” true?

In Records of the Grand Historian, the joint biography of Han Xin and Lu Wan details how Lu Wan, though close to Emperor Gaozu from humble days, eventually became suspicious and defected: 'Han Xin and Lu Wan were not of a generation that accumulated virtue and goodness; they seized temporary opportunities and achieved success through deceit and force... Internally suspected because of their power, externally relying on barbarians for support, thus they grew distant and fearful, and when their schemes were exhausted and wisdom failed, they finally fled to the Xiongnu. Is it not lamentable!' In History of Han, the joint biography of Han, Peng, Ying, Lu, and Wu places Lu Wan among the five non-imperial princes, with a general assessment: 'All seized temporary opportunities, achieved success through deceit and force, and were granted territories, facing south as lords. Suspected by the powerful, they could not feel secure, and when circumstances became desperate, they plotted rebellion and ultimately perished.'