The thing about that hypothesis is not that it's a dark horse hypothesis that's heroically managed to stay un-falsified. It is, instead, a tiny remnant of what used to be the dominant and only type of hypothesis: that the brain (or some other organ) is a vessel for an independently existing spiritual entity.
Imagine that you're an alien explorer. You find, on a deserted planet let's say, an object with various knobs and dials, from which sounds emanate. You decode the sound and find that it is a voice giving reports of events in a civilization, such as the rise and fall of the "stock market" and the political careers of various leaders. You turn some knobs and the device plays music instead, or presents multiple voices conversing about various topics including the fortunes of various competing sports teams, interspersed with commercials.
Examining the inside, you see various components, none of which look very complex but are unfamiliar to you. You can tell there's power flowing in there, but you don't know how any of it works. There are no other emanations from it besides the sounds that you can detect, and no incoming patterns of signals that you can detect that correlate with the output in any way.
You conclude that it is a radio, or at least a radio-like receiver even if you cannot otherwise detect the signal it's supposedly receiving. That's a reasonable conclusion, very similar to what humans concluded about the brain up until a very few centuries ago.
But then, further research starts presenting challenges to that view. It's discovered, for example, that manipulating the components inside the device can cause the stock market price being reported in the news reports to go up and down. Similar manipulations can also change the instrumentation, tune, or lyrics of the songs, or determine which sports teams have winning seasons, or change the prevalence of commercials. And microscopic examination of the components gradually reveals them to be far more complex than they appeared. They actually have vast information storage and information processing capabilities.
There is no choice but to revise your hypothesis, and to conclude that as hard as it is to believe, everything you're hearing from the "radio" is actually coming from processes going on inside the device. There are a few who hold out hope that the explanation is actually that the device is a transmitter as well as a receiver, so that when the components are manipulated, the civilization or entity in communication with the device notices the change and responds accordingly. But the failure to detect any such transmissions in either direction, or any such entity in the vicinity, and the overall predictive success of physical models suggesting that even an unknown type of influence could not propagate faster than the speed of light, loom larger and larger against that notion.
That's where we stand with mind, consciousness, and the brain. The "vessel" hypothesis was once the only respectable possibility, and has steadily lost standing to the point where the only thing, absolutely the only thing, it has going for it is that when allowing arbitrary additions of unknown un-evidenced phenomena and entities, it cannot be entirely disproven.
