Is “Sleeping on firewood and tasting gall” true?

The original text of the Records of the Grand Historian, 'The Hereditary House of King Goujian of Yue', only records: 'After Wu pardoned Yue, King Goujian of Yue returned to his state. He then afflicted his body and worried his thoughts, placed gall in his seat, and whether sitting or lying, he looked up at the gall, and when eating or drinking, he also tasted it.' The official history has 'tasting gall' but not 'sleeping on firewood'. The two characters 'sleeping on firewood' first appear in Su Shi's 'Letter in Response to Sun Quan's Letter to Cao Cao' as 'sleeping on firewood and tasting gall, determining the time of death', which is unrelated to Goujian. It was not until the Ming dynasty's Chronicles of the Eastern Zhou Kingdoms, chapter 80, that 'sleeping on firewood' and 'tasting gall' were formally listed together as Goujian's act of revenge.