I think the main error is in people trying to explain a complex machine through one mode of "how it works". The second error is people trying to accuse other people of doing that.
Today, anyone with half a brain and an ounce of interest could look at any of the large machines that operate in their environment - buses, trains, construction equipment - and quickly discover that such machines have fluids being pumped, air being pumped, mechanical linkages and electric circuits used for both power delivery and control, many or all of these things having - at a higher level - feedback loops designed in for autonomous control/self-balancing, and of course there's a whole economic and social layer on top, that's key to explaining why the machine works the way it does.
Why wouldn't it be any different with the human body?