This is not entirely correct. The eye+brain (I include the eye because it is my understanding that some "post-processing" of the image data takes place in the retina) does some color correction even though it is incomplete. I had an experience that illustrates this: After shooting some soldierfish in a mini-cave in the side of submarine lava flow formation (Big Island) I decided to chimp to see if my flash exposure was correct as there was time to re-shoot in case I screwed up. The lava formation was large enough that I was in its shadow so the light was very blue even though it was not too deep. When I looked at the image on the camera's screen the soldierfish appeared day-glow orange. I later re-checked these images when I got topside and the orange color was normal. My eye+brain had been compensating for the rather blueish light. Recall also that when you shoot under tungsten lighting the image will be rather red unless the WB is set to tungsten. However we do not perceive all this redness with our vision. Our eye+brain is doing some color correction.
. Because usually and without lights we dont see reds more than the camera sees it,we dont see a white balanced image.
So if its not there anyway why do we try to create it (can also use fake it) and try to give to to the audience, whatever that audience is, a fake white balanced image.
Tom you are absolutely right that the brain is always white balancing.
When we are subjected to an image that is biased towards one particular colour then after a few minutes our brain starts to white balance the colours, trying to minimise the more prevalent colour and boosting the other two primary colours.
This is why we often think that our images looked better on the camera when we recorded them underwater and then we download the footage afterwards and are disappointed in how the colours look on our computers, it is because our brain is white balancing while underwater.
Colour also plays a psychological role in our videos, we perceive dark green to be dangerous and edgy, yet a more neutral white balanced image has a calming effect on us & therefore is usually more appealing.