I won't lie -- I have a very strong intuition that there's this visual field in front of me, and that I can hear sounds that have distinct qualities, and simultaneously I can feel thoughts rush into my head as if there is an internal speaker and listener. And when I reflect on some visual in the distance, it seems as though the colors are very crisp and exist in some way independent of simple information processing in a computer-type device. It all seems very real to me.

I think the main claim of the illusionist is that these intuitions (at least insofar as the intuitions are making claims about the properties of qualia) are just radically incorrect. It's as if our brains have an internal error in them, not allowing us to understand the true nature of these entities. It's not that we can't see or something like that. It's just that the quality of perceiving the world has essentially an identical structure to what one might imagine a computer with a camera would "see."

Analogy: Some people who claim to have experienced heaven aren't just making stuff up. In some sense, their perception is real. It just doesn't have the properties we would expect it to have at face value. And if we actually tried looking for heaven in the physical world we would find it to be little else than an illusion.