Is “Hua Yuan entered the Chu camp at night, seized Zi Fan, and revealed the true situation to repel the enemy” true?

According to the Records of the Grand Historian, 'The Hereditary House of Song Weizi', when Chu besieged Song for nine months and the city was in danger, Hua Yuan entered the tent of the Chu general Zi Fan at night, climbed onto his bed, and reported the emergency. Zi Fan asked about the real situation in the city, and Hua Yuan replied, 'We are splitting bones for firewood and exchanging children for food.' King Zhuang, moved by his sincerity, lifted the siege. In the Chronicles of the Eastern Zhou Kingdoms, Chapter 55, it is written that Hua Yuan climbed onto Zi Fan's bed at night and truthfully said, 'Hua Yuan said: "We are exchanging children for food and picking up bones for fuel; we are already in dire straits."' This led to the oath between Song and Chu and the retreat of troops. The plot originates from the official history.