I would like to return to the original questions regarding this subject....the concept of "introspective illusion." I ran across this idea while researching the idea of the "adaptive unconscious," while looking into that book, Blink!... The principle underlying the introspective illusion would appear to be precisely what I have been after with regard to the the philosophical concept of "privileged access."
I think both. If we accept that conscious awareness is a subset of cognition—which includes the cognitive unconscious—is just the tip of an iceberg, with even the iceberg not capable of apprehending the “whole,” then that bears on claims to privileged access to some whole or full consciousness it itself.