It's a great question, and I think this is a pretty good insight into the general state of the field of neuroscience at the cellular level. We know a lot of details about things going on inside neurons, and a lot of details about synapses. And these details are often specific to one of the hundreds of different types of neurons that are found in different parts of the brain. (e.g. http://www.neuroelectro.org/neuron/index/). And we do have methods to measure and manipulate various things in neurons in a dish. But the dynamics of a neuron's voltage are complicated, non-linear, and time-varying, and there are many parameters (e.g. the concentrations of numerous ionic species and other small molecules, many of which we probably don't even know about yet).

Even then, going from these messy biological details (e.g. these 20 proteins assemble into a particular form and release this neurotransmitter from this synapse when X happens) to an explanation for how the neuron works at a more algorithmic level is hard, and the field isn't there yet. Assembling and abstracting the details is hard and it's one of the goals of theoretical neuroscience. The complexity is probably a symptom of our lack of understanding, rather than the cause of it, i.e. there probably are a lot of details that we can abstract away in a simpler functional model.

I haven't read the paper, and I'm only vaguely familiar with Hawkins et al.'s HTM work. But I disagree with the claim at the end of the TR piece that these predictions are imminently testable. Thinking up a specific experiment to try and disprove theoretical ideas is often the hardest part of experimental neuroscience.