Is “Lian Po once bared his back, carried brambles, and asked for punishment, becoming sworn friends with Lin Xiangru.” true?

The Records of the Grand Historian, Biography of Lian Po and Lin Xiangru, clearly records: 'When Lian Po heard of this, he bared his back, carried brambles, and through a guest went to Lin Xiangru's door to apologize... In the end, they became friends and were sworn to death.' The Chronicles of the Eastern Zhou Kingdoms, Chapter 96, directly copies this historical fact, and the novel does not deliberately exaggerate.