The camera is behind and "below" Saturn, and Saturn's rings are "tilted" towards the Sun (you can see this because the planet's shadow on the rings is curved; if the ring was parallel to the light rays, the shadow would have straight edges).
The planet's back is lit by the rings: the upper part gets light reflected by the rings, and some diffused light, while the lower part only gets diffused light, that's why the upper part is better illuminated.
The "black rings" that you can see over the upper part of the planet are just the back of the rings (i.e the part that's in Saturn's shadow). Because the planet is much better illuminated than this portion of the rings, you see them as black on colored background (they must receive some light from the back of the planet, but that's probably below the sensitivity threshold of the camera).
They are "offset" because you only notice the portion between the camera and the planet; the rest of the shadowy part of the rings is dark on a dark background, so you can't see it.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/tn7VSUK47vM/story01.htm
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