I want to see a cats POV when its startled by a cucumber (Youtube has lots of examples). A theory is that part of the brain mistook it for a snake. Also research on "constant bearing, decreasing range (CBDR)" where drivers may not notice another car/cycle in a perfectly clear crossroads till its too late.'
For something like these kinds of reflexes, my understanding is that the response comes from the central nervous system, even before the brain has had the chance to fully process the input. This shortcut makes one avoid, say, burns or snakes, quicker than if it required the brain. Still, I agree with you that seeing what a cat sees (here or anywhere) would be awesome.
I think the distinction you're drawing between "the central nervous system" and "the brain" is mistaken here -- the brain is part of the CNS. This kind of reflex basically has to involve the brain b/c it involves both the visual system and the motor system i.e. there's not a fast path from the retina to moving your appendages etc that doesn't include the brain.
The "fully process" part is part of the story though -- e.g. perhaps some reactions use the dorsal stream based on peripheral vision while ventral stream is still waiting on a saccade and focus to get higher resolution foveal signals. But though these different pathways in the brain operate at different speeds, they're both still very much in the brain.
Yeah I think there are multiple documented cases of this, where especially well-practiced motor-plans seem to be 'pushed down', and if they're interrupted, correction can start faster than a round trip to the brain.
Reflexes do not necessarily have to exist in the brain, but they do exist in the central nervous system. The peripheral nervous system doesn't handle reflexes as far as I'm aware.