Is “When Yan Ying was sent as envoy to Chu, facing the insult 'Is there no one in Qi?', he retorted, 'When one is sent to a dog country, one enters through a dog door.'” true?

The classic episode of Yanzi's mission to Chu originates from the "Yanzi Chunqiu, Inner Chapters, Miscellaneous Part II"; the "Records of the Grand Historian, Biographies of Guan and Yan" contains no such account of the mission to Chu, nor the witty repartee about the dog gate or the orange trees south of the Huai River. This plot belongs to the persuasive fables of the pre-Qin philosophers, later absorbed by novelists. The novel writes: "此狗门，非人所出入也！使狗国者，从狗门入﹔使人国者，还须从人门入。" (This is a dog gate, not for humans to enter or exit! One who is sent to a dog country enters through the dog gate; one who is sent to a human country must still enter through the human gate.) From "The Romance of the Eastern Zhou Kingdoms," Chapter 69.