> But doesn't this rely on the same thing you suggest we don't have, which is a working and definable definition of consciousness?

No, it's like saying we have no indication that humans have psychic powers and can levitate objects with their minds. The commenter is saying no human has ever demonstrated the ability to figure things out that aren't Turing computable and we have no reason to suspect this ability is even theoretically possible (for anything, human or otherwise).