I don't think you have to worry Matthias, about falling off your functionalist track when studying brain parts. ;)
Brain parts can't do much in isolation - they need to grow up with and be constantly stimulated by other brain parts in order to do anything, plus they seem to need to have that nice steady stream of 10,000 new neurons a day folded into the mix to keep the entirety working well. It seems to me that brain as a whole is much less about "parts" and much more about "function" than the rest of the body:
1. Some "parts" can take over for other "parts" in a pinch.. I met a young woman a few years ago who had had a hemispherectomy for extreme epilepsy as a young child. The remaining half had taken over function quite readily.
2. Constraint induced movement therapy (CIMT) can retrain remaining parts of the brain to take over from parts that have been wiped out by stroke. (For more on this you can listen to Ginger Campbell's podcast interview with Edward Taub, the originator of this form of therapy, in her brain science podcast #28.)
It seems to me that neuroplasticity is such a feature that it likely may have been and in many cases likely still is a confusing factor for researchers who really, really want to find direct relationships between brain parts and functions.
I know where you're coming from - I'm a PT too. We started out being taught structure - "This is the knee joint. It bends thusly. It is covered in cartilage to make movement smoother." Etc etc...
What helped get me out of this structuralist mind set training was embryology. The physicality of the body we deal with as PTs is a blend of mesodermal and ectodermal derivatives (well, endodermal too, but we don't deal directly with or concern ourselves with endoderm much.)
We get taught all about the mesodermal derivatives (overwhelmingly!) in school: mesoderm derivatives account for 98% of the whole body. Their structure IS their function.. unfortunately the educators don't realize what they are doing to our poor brains! :D
Direct ectodermal derivatives, by contrast, account for only 2% of the body's mass - and that includes outermost layer of skin, brain, spinal cord, and all the 45 miles of nerves that lace throughout all that mesoderm. We have a brain 5 times BIGGER than needed to operate a mammal our size - and still, direct ectodermal derivatives account for only 2% of mass! That's tiny!
However (and this is a very clear distinction), direct ectodermal derivatives use 16%-20% of all the oxygen taken in. (Streidter, Principles of Brain Evolution) That's huge! The nervous system and the rest of the body are clearly out of proportion here. Big, big difference physiologically.
This is still astonishing to me, every time I think of it. What a busy system. What a huge oxygen sink our brains are, so big and so busy. So "functional". Function is its business - brain "structure" is less relevant by comparison. In fact, sometimes when I remember that fact that humans have a brain 5 times bigger than necessary for operating a mammal our size, I wonder if its high-maintenance oxygen-neediness contributes to most of our problems..
Anyway, back to the point - I don't think brain parts can be classified into "this part does this, and that part does that" as easily as the rest of the body can. And everyone, at all times, will do well to remember that correlation does not = causation. One notes when reading papers that the authors are usually very careful to skirt around declarative statements such as, "the x part is responsible for y." Instead they say something like, "Y was found to be associated with abc waves in the z frequency when neurons in the x part were stimulated" or "when the animal exhibited x behavior." That way, they can describe a relationship between parts and function, but don't run the risk of sounding prematurely categorical or final.
"If you think about patients with chronic pain it all starts making sense:
pain leads to stress - stress leads to gray matter loss in the brain (not just in the hippocampus) - thereby limiting the amount of neurons you have to be able to learn something new. It really is a vicious circle. Scary stuff."
But, maybe stress can also lead to pain... or maybe neuron loss in the brain can lead to less adaptation to stress which might lead to pain... I don't think anyone has it figured out for sure yet. It's really all one great big circle of function/adaptation. As Quinter et al. have said, pain seems to be an aporia. (Not that we can't do something to help!)
One thing we can take comfort in (as PTs) is that movement appears to be associated with better brain function as well as all sorts of other health benefits. Motion is lotion for the brain/nervous system, not just the joints. :)