Question

We learned at the beginning of tractate Menachot:
 
“All meal-offerings whose handful was taken not for their own sake are valid, except that they do not count for the owners toward fulfilling their obligation, except for a sinner’s meal-offering and a jealousy meal-offering.”
The Talmud on 4a brings Rav’s view that the omer meal-offering as well, if its handful was taken not for its own sake, is disqualified, because it comes to permit and it did not permit. The Talmud asks: why didn’t the Mishnah spell out: “except for a sinner’s meal-offering, a jealousy meal-offering, and the omer meal-offering”?
The Talmud answers:
Because when it teaches, it teaches about an individual offering; it does not teach a communal offering. When it teaches, it teaches something that comes on its own account; it does not teach something that comes because of a sacrifice. When it teaches, it teaches those for which no fixed time is set; this one, for which a fixed time is set, it does not teach. “The omer meal-offering is not similar to the other meal-offerings, since it is a communal meal-offering,” etc.
What is the meaning of the Talmud’s answer? Does it mean that the expression “all the meal-offerings” at the beginning of the Mishnah includes only individual meal-offerings that have no fixed time, and communal meal-offerings are not included at all in “all the meal-offerings”? If so, it needs clarification why the Mishnah did not limit the rule.
Perhaps one could also say that the Mishnah excluded by the phrase “except for” only individual meal-offerings, but not communal meal-offerings, and again one needs to understand why the Mishnah did not emphasize this.
Thanks in advance