I do think that the astonishing hypothesis is half wrong (well, half wrong for human beings, completely wrong for matter in general, in that matter is a sensory experience, not the other way around.) but yes it sounds like we agree on the non-computational, or trans-computational nature of qualia.
Something like a brain scanner is only giving us a view of certain conditions, like magnetic resonance and blood oxygen levels, through which we can infer the brain or conscious experience. It would be like programming a Google car to drive through Paris, taking pictures of all of the road signs, and by putting these signs in order and correlating them with our visits to Paris, we can imagine that the signs play a key role in the functioning of French culture.
We could find all kinds of interesting patterns about where and when certain cultural events happen by sending more Google cars into Paris, comparing maps of the road signs to Tweets and blog posts on the internet. The goal is to come out with a master list which correlates each road sign and each position to the specific functions of French society - the fashion, the food, the language, the art, etc. The fact that this can be done, while useful in actually being able to fix French cities more effectively if they are damaged, does not mean that the assumption of a causal connection between road signs and culture exists. In reality, road signs refer to narrow, local conditions related to driving, not mechanisms for building the Louvre.