Is “When Wu Qi was a general in the state of Lu, because his wife was from Qi, to dispel the doubts of the Lu monarch and ministers, Wu Qi killed his wife to show his resolve.” true?

According to the Records of the Grand Historian, Biography of Sun Tzu and Wu Qi: 'The people of Lu doubted him, so Wu Qi, seeking fame, killed his wife to show he had no ties with Qi.' Such heartless, cruel, and unscrupulous acts are clearly recorded in official history.