That direction would likely contain weird outcomes if the science progressed, something like "Dogs are barely-conscious due to their pack structure, they have a couple levels of recursive theory of mind but they can't sustain it as deep as we can. But cats didn't have that pack structure, they're not conscious at all." Or, "this person has such severe autism that he cannot fundamentally understand others' minds or what others interpret his mind to be, so we've downgraded his classification to unconscious. He'll talk your ear off about the various cars produced in a golden age between 1972 and 1984, but because he doesn't really know what it means for you to be listening we regard it as sleep-talking."
It also just kind of doesn't sound right. "What happens when we go to sleep? Well, we stop thinking about what others think we think, and we simply accept what they think about us." That doesn't sound like any sleep I experience -- it might describe some of my dreams, but of course dreams are anomalous conscious experiences that happen during sleep so that also misses the mark.