There are two aspects to this. First is neuroscience. Jeff Hawkins has published several peer reviewed papers. But it is too new to establish itself in the field as an accepted theory.
See various papers referenced in this article.
As to what it means to ML in general is unknown. The ML community has largely ignored this until now. It has become common practice now to let researchers / labs get involved in commercializing their discoveries. Nothing wrong with this per se. Afterall people who push current NN also have a lot of commercial interests. But the basic observation that our brains behave very differently than NN is obvious
- You don't need a million pieces of data to learn new things
- You can do object recognition and learning at the same time
- etc
Whether it is their theory that explains the difference or something else remains to be seen.
There are solid arguments against Backpropagation artificial neural networks as models of actual brain function despite having come out of a Psychology Department (specifically the Cog Sci program at UCSD). Though Backprop is of course a powerful tool.
The gold standard of neurophysiogically plausible brain modeling is that of Stephen Grossberg mostly done in the Cognitive and Neural Systems Department (while it was around) at Boston University.
Grossberg's approach uses non-linear differential equations to describe neurons organized into layers of various topologies. The topologies are usually designed based on some neurophysiological correlates, i.e. the neuroanatomy of the relevant parts of the brain, as well as some target performance data. The target data, usually sets of psychophysical measurements or psychological observations, is simulated on a computer using numerical integration.
The approach has yielded compelling results in almost all areas of brain function: memory, cognition, vision, behavioral conditioning, motor control, rhythmic behaviors, ...
One of the simpler and more accessible models that will give a taste of the approach is the Vector Integration to Endpoint (VITE) model of Grossberg and Bullock. It shows how neurons might create the bell shaped velocity profile observed in, say, an arm reaching movement.
Grossberg produced with his numerous collaborators a very large body of work. One place to start is "Studies of Mind and Brain" (D. Reidel Publishing Co. 1982) though there are many later works as well.
It can be heavy sledding but worthwhile for those interested to see how much we already can replicate of human brain function including some its very sophisticated processes.
Tl;dr There is not a "Theory of Human Body Functioning," rather there is a set of interconnected complex systems to be understood.
Similarly, those seeking or touting a single overarching theory of brain functioning are generally early in their journey towards understanding what we know of the brain.