This is in your review of the daf on 64b:
5. Question: (If so, 1/4 Kav wheat makes 2 meals) - 2 Kabim are 16!
i. Suggestion: Our Mishnah is as R. Chidka, who says that a person must eat 4 meals on Shabbos.
6. Rejection: No, our Mishnah can be as Chachamim - the extra meal is for guests.
The Rashi on that suggestion says that it is a bitmiya, implying that the Gemara doesn't like that possibility, which is understandable since Rav Chidka is a daas yachid. However, if the gemara doesn't like that possibility here, then how come on the next line, the gemara says that Rav Shimon will work out also and you get 18 if the 3 extra meals are for the guests according to the Chachamim or the 2 extra meals according to Rav Chidka. Why bother mentioning Rav Chidka again if the Gemara didn't think that was a viable answer the line before.
David Greenstone, St. Louis, MO, USA
The practice of the Gemara is to try to interpret any Stam Mishnah like all of the opinions on any particular matter, in order to show that proof cannot be brought from this Mishnah to either of the opinions.
The Gemara therefore tries to avoid saying that the Mishnah can only be reconciled according to Rav Chidka. Similarly, the Gemara tries to avoid saying that the Mishnah can only be reconciled according to Rebbi Yochanan ben Berokah. And once it says that it could be reconciled even according to Rebbi Shimon, the Gemara goes further and shows that the Mishnah may be reconciled according to Rebbi Shimon regardless of whether Rebbi Shimon holds like Rav Chidka or like the Rabanan who argue with him.