I don't actually think the commentator you responded to is arguing for either of these narratives and I thought it was a pretty useful way to look at some of these arguments.
It doesn't need to be true but a lot of people make it/assume it.
There's a lot of, perhaps casual and uninformed, conversations that strongly imply a deeper understanding of the "physics" of brain chemistry than we actually have, mostly by comparing it to machines we've constructed.
(I believe) We don't need to replicate human neurons and dendrites and whatever else is in there in order to create a sapient "machine", but whether or not we've actually done that isn't being helped by arguing that what we currently have is all that similar to a human brain.