Firstly, in spite of what the Beano says, there is not a little person inside you looking at a screen on which your field of view is projected. Here's a picture of what's not happening:
As far as we're concerned, we are the whole world. Nothing in our physical Universe is not in a sense part of us except for the worlds of others. Consequently, we cannot "step outside" our world and see ourselves from outside. The visual world is what there is for us, and there is nowhere beyond it where it will seem to be inverted. There are holes in our world of course, in the form of other people, but apart from that, we are the Universe, which is one reason why murder is so wrong - kill one person and you destroy a whole Universe. Incidentally, this also means that attempting to add deaths up is questionable. People are not interchangeable, which to me seems to undermine the whole basis of utilitarianism. That's another story though.
The less philosophical point about this is that whereas there is in a sense an image of what you see inside your brain, it never, ever gets turned the "right way up". Instead, the signals from the rest of your body get turned upside down! Here is a sketch of the area of the brain which interprets the touch signals from one side of your body:
This is referred to as the sensory homunculus. There is also a motor homunculus, which represents the quota of fine control provided to different muscles in the body, and looks like this:
So, what in fact happens is that the visual representation in the brain doesn't get turned upside down at all, although it does get sliced in half and sent to opposite sides of the brain. Instead, everything else is turned upside down, which also results in most of the body being reflected in the brain so that the left hand side of your body is connected to the right hand side of your brain and the right hand side of your body is connected to the left hand side of your brain.
Nevertheless, Cartesian though it may be, the Numskulls are a fun comic strip even if it does mess with your head. Who is inside the Numskulls' heads? Who is inside the meta-numskulls? And so on.
Oh yeah, the video. Here it is: