Is “Duke Xian of Jin believed Li Ji's slander and forced Crown Prince Shensheng to commit suicide.” true?

According to the Records of the Grand Historian, 'The Hereditary House of Jin', Duke Xian of Jin was infatuated with Li Ji and wanted to make Xiqi his heir. Crown Prince Shensheng offered sacrificial meat to his father. 'When Duke Xian was out hunting, the meat was placed in the palace. Li Ji had poison put in the meat.' When the Duke tested it, a dog died and a servant died, so he became intent on killing Shensheng, who hanged himself. In the Chronicles of the Eastern Zhou Kingdoms, chapter 27, it is written that Shensheng presented the meat, and 'Li Ji put poison in the wine and smeared poison on the meat.' When the Duke saw the dog die from eating the meat, he ordered a strongman to smash the original bearer with a hammer. Shensheng, without defending himself, took his own life. The plot is consistent with the official history.