Is “After Zheng shot and wounded the King of Zhou, did they continue to pursue?” true?

The Records of the Grand Historian, 'Annals of Zhou', Part II, only records: 'In the thirteenth year, [Zheng] attacked Zhou, and Zheng shot and wounded King Huan, who withdrew and returned.' However, in the ninth chapter of Chronicles of the Eastern Zhou Kingdoms, it adds that Duke Zhuang of Zheng sounded the retreat and explained: 'Duke Zhuang said: "Originally it was because the Son of Heaven was not enlightened, turning virtue into resentment. Today we resist the enemy, it is absolutely unavoidable. Thanks to the strength of all the ministers, the state is not lost, that is enough. How dare I ask for more! According to your words, if we capture the Son of Heaven, how should we deal with him? Even shooting the king is not permissible. If he is severely wounded and dies, I would bear the name of killing the ruler!"'