I don't think the use of the word "expose" in that sentence is meant to assert that the core of satire is that it must be right. Satire is a type of media/expression, it would make little sense to have a taxonomy of media where what genre something is depends on the personal political affiliations and beliefs of the observer, where saying what genre something is in is a declaration of those beliefs.
Why object to calling it satire? It's obviously closely copying the format of other media primarily known by that label, I don't think there's any other term that works as well to describe what sort of thing it is.