Is “Zong Chuke protested against impeachment in court, and Emperor Zhongzong ordered him to become sworn brothers with the censor.” true?

According to the 'New Book of Tang, Biography of Zong Chuke', Censor Cui Wan impeached Zong Chuke for bribery in the court. According to regulations, a minister impeached by a censor must leave the court and await punishment. 'According to precedent, when a minister is impeached by a censor face to face, he must hurry out and stand in the court awaiting punishment. But Chuke, with a stern expression, loudly said: "I am by nature loyal and upright, and have been slandered by Wan." Emperor Zhongzong could not get to the bottom of it, and issued an edict ordering Wan, Chuke, and Chu to become sworn brothers to reconcile the matter. Thus, the world called the emperor the "Peacemaking Emperor".' In Chapter 77 of 'Sui and Tang Romance', it is written that Cui Wan impeached Chuke, and Emperor Zhongzong 'only ordered Cui Wan and Zong Chuke to become sworn brothers to reconcile them. At the time, people spread it as a joke, and therefore called him the Peacemaking Emperor.' This comes from the official history.