Is “Before marrying Yiren, Zhao Ji was already pregnant with Lü Buwei's child, and Qin Shi Huang was actually Lü Buwei's illegitimate son.” true?

The Records of the Grand Historian, Biography of Lü Buwei, explicitly states: 'The lady concealed her pregnancy, and when the full term came, she gave birth to Zheng.' Sima Qian wrote this palace secret into the official history, leading many novels to adopt this account. Although modern times have raised doubts, this is indeed what the official history records.