No, Meta's legal team didn't claim that its fact-checking labels are "just opinions" or "just protected opinions". The word "just" doesn't appear in connection with the word "opinion" in the legal document that the article used as a source.
The document does claim that the fact-checking labels are "protected opinion", which is a term of art in U.S. defamation law. Its meaning is defined by the legal code and by previous judicial decisions, not by vernacular use of the word "opinion". (Judicial decisions are, incidentally, also called opinions in law, even when they're legally binding.)
I think that there is a parallel here to the common claims that evolution is "just a theory". Of course, scientists never say that evolution is just a theory. They do say that it's a theory.
The Digital Media Law Project's article about Opinion and Fair Comment Privileges includes this example of a protected opinion: "Danielle is failing out of school because she is a blond and the only thing I ever see her do at the library is check Facebook." Note that "Danielle is failing out of school" is considered an opinion, and that it doesn't matter if it's wrong and your reasoning is stupid, but it does matter that you cite the true facts that are the basis for it. Meta argues that it did so by linking to articles published by Climate Feedback.
Even the definition of "opinion" in general-purpose dictionaries seems broad enough to cover the legal use. Merriam-Webster online has "a view, judgment, or appraisal formed in the mind about a particular matter" as its first definition.