This bit is important -- it might be that "within the field" of postmodern literary criticism (for example), some idea 'X' is accepted as a matter of course, and that no one within that field questions it. But outside the field, others may find reason to dispute it vigorously.
No, that's not a fair example, as postmodern literary criticism is just one camp in the study of literature. But if all camps - that is, nearly everyone who was an expert in literature - accepted some particular claim about literature, then that claim could probably be stated with no qualifiers (I suspect there are very few such claims in literary study...)
Here the question is - does nearly every expert in whatever field "global warming" falls under (environmental science, or whatever) accept William Connolley's claim? I don't know yet.