How does déja vu, that is the re-experiencing an experience, fit into this theory? It appears that the Information axioms fails to be Essential when one considers déja vu.
Given this, the simplest and most compelling explanation is that the brain has somehow short-circuited itself into invoking a sense of familiarity. Otherwise I'd expect, at least some people, some of the time, to be able to either link the two experiences or make predictions. The claim that exactly the same experience has actually occurred twice is the more remarkable, both in terms of evidence and plausible mechanism.
Whilst I do appreciate that experiences are highly subjective beasts, it doesn't feel like this really challenges the linked article. Besides, if one is so wedded to the subjectivity of experience, they might as well just say that nothing can objectively explain consciousness because it's subjective, end of.