Is “Framed by Fei Wuji's slander and forced to flee” true?

The Records of the Grand Historian, in the biography of Wu Zixu, records that after Fei Wuji procured a beautiful woman from Qin for King Ping of Chu, he advised the king to marry her himself to curry favor, and then, fearing future retaliation from Crown Prince Jian, slandered him day and night, causing him to flee. The novel faithfully preserves the historical context and causality of Fei Wuji (Wuji) bearing a grudge against the crown prince over the Qin woman affair, and subsequently repeatedly slandering Crown Prince Jian, ultimately leading to his exile. The original text: 「使太子建居城父，守边。无忌又日夜谗太子建於王曰：“自无忌入秦女，太子怨，亦不能无望於王，王少自备焉。且太子居城父，擅兵，外交诸侯，且欲入矣。”」（《史记·楚世家》，data/raw/shiji/楚世家.txt）