Is “Wu Sansi had an illicit affair with Empress Wei, played double-six, and was killed” true?

The New Book of Tang, Biographies of the Five Princes, records: 'At that time, Wu Sansi, because he had been moved by the Empress Dowager's resentment, feared harm to the various Wu, and Empress Wei was deeply favored and feared by the emperor, and Sansi had an illicit affair with her, thus they slandered and hit their targets.' In chapter 75 of the Sui and Tang Romance, it is written that Emperor Zhongzong returned to the palace and saw Wu Sansi and Empress Wei 'sitting facing each other in a game.' Zhongzong laughed and said, 'You two are quite at ease, playing double-six here.' Later, Sansi was killed by Crown Prince Li Chongjun, which is consistent with the official history.