The idea that the human body is an organism isn't problematic scientifically or philosophically, it's only a problem religiously. What is the brain of a computer? The CPU? The CPU and the GPU? The CPU, GPU, and RAM? etc, etc. It makes much more sense to assume interdependence in an organism than some sort of weird "operational independence" or however you'd like to phrase it. The computer as a poor analog is easy enough to appropriate to approach thought experiments.
Very good analogy, thanks. Much better way of framing what I said in my first comment. I'm thinking in future ages, people will look back at how primitive we were assuming that the pinnacle of human intelligence and personhood was contained in the brain. Much like we look back on people in olden times who thought emotions were situated in the heart.