(Presumably your first "that" is meant to be a "what"?) That question implies a false dichotomy too. The mistaken people might not be mistaken about what anyone thinks unmediated experience is; perhaps everyone pretty much agrees on what it is, and the mistaken people are simply misremembering or misinterpreting their own experiences.

This conversation might be more productive if you switch from Socratic questioning to simply presenting a reasonable definition of "unmediated experience" according to which unmediated experience exists. After all, your true objection seems to be that I'm using a bad definition.