"[i]f you look closely at our nervous system, you’ll see that there are neuronal clusters distributed throughout the body. Human computation is better understood as distributed than centralized."
It's kind of like having a computer at the home, but tens of thousands of computers at a data center. Things like reflexes can happen quickly because you don't have to go all the way to the brain, but your arm isn't going to be adding 2+2 by itself.
It's almost entirely in your brain. Less "your muscles remember how to do things" and more "your brain remembers how to do things using your muscles".
The muscles and the nerves within your limbs adapt some - they respond to being used - but they don't have the representation capacity to store action patterns in them.
The spine itself is another matter - it's much more complex and adaptive, it has some capacity, it can learn things. It mostly carries a set of reflexes you get at birth, and some commonly used learned action patterns. Less "how to play the piano" and more "a set of finger motions useful for playing piano". The most studied thing is probably the spinal involvement in gait generation and stabilization of bipedal locomotion.
Now, things would be different if you were an octopus. But humans are pretty centralized, as far as nervous system goes.
