How do the Records of the Three Kingdoms represent the Battle of Chibi/Red Cliffs?

The battle of Chibi, quote de Crespigny:
The whole aﬀair became a theme and a source for many plays and took a central position in the celebrated Romance of the Three Kingdoms. It is now difficult to discern the reality behind the accretions, whether fact or fiction, and certainly hard to assess the nature and scale of the defeat.
Contrary to the grand scheme in Romance, the record of 3 kingdoms is very brief and anti-climatic about the battle, as it tend to be about everything else.
In Sun Quan's biography (book of Wu): At that time, lord Cao had assimilated the army of Liu Biao, his force was so overwhelming that everyone was terrified; a lot of officer advised Sun Quan to surrender. Only Zhou Yu and Lu Su advised to fight, which Sun Quan agreed. Zhou Yu and Cheng Pu assumed the title of left and right admiral, both leading tens of thousand men, joined forces with Liu Bei. They face Lord Cao's army in Chibi and soundly defeat him. Lord Cao burned the remaining ship (to prevent them being captured by the enemy) and retreat. The men were suffered from starvation and sickness, more than half of them was dead.
In Cao Cao's biography: the lord (Cao Cao) came to ChiBi, fought Liu Bei and was at disadvantage (in Records, this phrase usually mean "was defeated"). At that time, there is a disease which killed a lot of soliders, so the lord retreated. Liu Bei occupied Jing province and districts south of Yangzte.
That's it. The famous fire attack may not even happened, instead, Cao Cao burned his own ships to prevent them falling into enemy hand. So where were all those infamous schemes in Romance come from? Luo did not invent all of it, he collected stories from different sources, then weave them into his own narrative. In case of the Chibi Battle, it seem that he drew most of it from Jiangbiao story - a work composes in Jin dynasty era, describes many events that Romance reader are familiar with: The debate fight/surrender and Sun Quan's dilema, Hoang Gai's fire attack... Later in Jiangbiao, Cao Cao sent a letter to Sun Quan to complain that he burned the ship on his own, yet Zhou Yu took all the credit for it! Well, of course Cao Cao would say that.
Jiangbiao story has very obvious bias toward Sun Quan faction, therefore probably not too creditable. de Crespigny use this source extensively when discussing Red Cliff in his Cao Cao's biography, yet he does not list it as a historical text. This story should not be trusted 100%, but so does Records of Three Kingdom. While Chensou has access to more official information, he is a officer from Jin dynasty - which take their legitimacy from Cao Wei. If Cao Cao lied that he burned the ship and not Zhou Yu, it is entirely possible that Chensou had to use this version when compiling Records of 3 kingdoms.
Now, we are left to speculate what happened. de Crespigny argued that some fighting did happen but it was mostly the disease that did the job. Nonetheless, Cao Cao was overconfident and oblivious to his army's actual combat effectiveness. When he was visited with a rude awakening by the coalition army or by the disease casualty report, he was in such a desperate situation that he had to burn his fleet. By doing so, he gave up control over the Yangtze. At the start of this campaign, Cao Cao had a more ship, more men; at the end of it, he would never be able to challenge Sun Quan's naval domination again.
Source:
de Crespigny, Imperial Warlord, chapter 6.
Record of three kingdoms, book of Wei & book of Wu