I agree with you however I think even then you're still giving our brains too much credit. The speed definitely comes from that processing being "in silicon".

Your ball throwing example however will be handled by really small and really fast "fine tuned agents" dedicated to catching that ball. Eyes to motor neuron system. There are the illusion of free will experiments that demonstrate your brain only rationalises and explains whatever activity took place after the fact (It's explanation may even be entirely wrong).