The Ultimate Form of Storytelling

So, my previous post was on the book Incognito, which I talked about in relation to criminal justice and the death penalty, but I realize now that I probably wasn't making all that much sense. I also realized that I missed what might not be a particularly shocking proposal to someone fairly well-versed in neuroscience, but is a very interesting claim:

Consciousness is  a story we tell ourselves.

Now, that's not to say that we don't have consciousness - obviously we do, but, as Eagleman puts it "we are constantly fabricating and telling stories about the alien processes running under the hood." Alien processes is a term he uses to refer to the many, many, many functions of the brain that run almost entirely without our knowledge, until we are fed the end product. Our consciousness then works to create a coherent story for us about all the input we're getting, that sometimes might contradict or otherwise require some explanation. 
One of Eagleman's best examples of this is in the case of split-brain patients (click the link if you don't know what that is). In one set of experiments, different pictures or commands were shown to the different hemispheres using some weird device. If, using this device, you flash the word "walk" to the right hemisphere, which is the now unconcscious part of the brain, the patient will get up and start to walk. However, they do not know they've been given this command, so their left brain, realizing that they are walking and don't know why, will quickly come up with a reason, such as "I was going to get a drink." This can also be seen in the excuses of anosognosia patients, of which Supreme Court Justice William O. Douglas is a particularly famous case.
There are myriad other examples of this storytelling in perfectly healthy people as well, and we are probably doing it constantly, without any idea. If we ourselves are just stories constructed by the tiny fraction of our brain that is conscious to explain the working of the rest of our brain, then what does that say about our ability to accurately perceive the world and construct stories about that?