I don't want to be too critical, because I've learned a lot from the author's books, but a fair amount of the article (mainly myths 1 and 2) seem to be over-generalization or skewed based on the author's bias. Her field is psychology, not primarily neuroscience; specifically, the psychology (and some neuroscience of) emotion. I recommend Jeff Hawkins's new book for a perspective closer to a neuroscientist's. (He's technically not a neuroscience Ph.D., but he has equivalent knowledge.)
Myth #1: Brain areas aren't separate and didn't evolve in stages.
1. Brain (neocortex) areas aren't single-purpose. Obviously neuroplasticity is a thing, but the article ignores that areas of the brain develop to be focused on a single category of tasks (visual, auditory, etc.). The author's example, blindfolding someone and watching their visual cortex get repurposed when learning to read braille, ignores that if you don't blindfold them, other areas will probably take up most of the task of learning braille because it's not a visual activity and the brain tends to separate areas of responsibility.
2. The number of significant evolutionary steps may not be just three, so the triune brain theory may be technically false, but I've never seen any actual neuroscientist argue that it isn't roughly accurate. The evidence in the article is molecular genetics: the fact that there aren't radically different kinds of neurons. This is like scaling up an argument that ethanol and glucose are the same thing because they share the same elements. If the limbic system and neocortex have roughly the same kind of neurons, what does that matter? We know they serve radically different purposes, and we know that reptiles don't have a neocortex (at least, nothing of significance).
Myth #2: Brain is stimulus/response machine
Her argument against this myth seems tortured. Of course the brain is not a simple impulse/response machine, but it's still essentially taking in inputs and responding in various ways. It just has a mind-bogglingly complex internal state.
Myth #3: Strong dividing line between diseases of the brain and body
Everything seems to point to her being right on this one. Science knows, nearly as much as it can know anything, that neurological stress leads to physical stress responses which can screw up other parts of the body, often through hormone dysregulation. Similarly, physical problems from gut health to inflammation can trigger immune responses or simpler biochemical reactions that have neurological side-effects. And, of course, diet. Psychoactive drugs are a clear example of how an external physical influence can have psychological effects.