First, some background:
In b.Hullin 104b - at the very beginning of the Gemara in pereq "Kol HaBasar" - there is a very strange and almost unintelligible section of argumentation which tries to prove that Rebi Yose is really the Tana Qama. However, in doing so it maintains that one could ask a question on the Mishnah that really does not seem at all possible.
The Mishnah there reads:
העוף עולה עם הגבינה על השולחן ואינו נאכל כדברי ב"ש וב"ה אומרים לא עולה ולא נאכל א"ר יוסי זו מקולי ב"ש ומחומרי ב"ה באיזה שולחן אמרו בשולחן שאוכל עליו אבל בשולחן שסודר עליו את התבשיל נותן זה בצד זה ואינו חושש
Poultry is put onto the table with cheese and is not eaten [together with it] according to the words of Beth Shamai, and Beth Hilel says it is not put [on the table] and is not eaten. Rebi Yose says, This is one of the leniencies of Beth Shamai and one of the stringencies of Beth Hilel. To which table are they referring? To the table on which one eats, but the table on which the food is set [to be served], one puts them side by side and there is no worry.
The Gemara then begins:
רבי יוסי היינו ת"ק וכ"ת אכילה גופה איכא בינייהו דקאמר ת"ק בהעלאה קא מיפלגי באכילה לא פליגי ואמר ליה רבי יוסי אכילה גופה מקולי בית שמאי ומחומרי ב"ה
Rebi Yose is the Tana Qama and if we say that this isur of eating is actually what is between them [i.e. what Beth Shamai and Beth Hillel are arguing about in the Mishnah], as if the Tana Qama suggested that that they were only arguing about whether they can be placed on the table together, but regarding eating they do not argue [i.e. they both agree that they cannot be eaten together], and Rebi Yose responds to him that [eating] is one of the leniencies of Beth Shamai and the stringencies of Beth Hillel [i.e. that Rebi Yose holds that eating them together is allowed by Shamai and forbidden by Hillel].
I am aware of Rebi Yose's own position elsewhere in Mishnah Hullin that poultry is not included in the isur of basar b'halav, but I am not sure that it has real relevance here.
Now, for the question:
When the Mishnah explicitly says that both Beth Hillel and Beth Shamai maintain that poultry cannot be eaten together, how can the Gemara then answer a hawa mina of reading the Mishnah to the opposite?
Further, do any manuscripts not contain this section? Are there any Rishonim or Aharonim that emend this text?
Thanks in advance. Kol tuv.