I've decided to compose the photo myself and show you exactly why it looks as it does.. I'm using the images listed in the penultimate paragraph of
this blog post from Emily Lakdawalla, the person who composed the original.
I start with three greyscale images, each of which has been taken using a red, green, or blue filter. To compose a color photograph, I'll have to assign each image to a RGB channel based on the filter that was used for the exposure. As you can see, Titan moved between exposures.

Now, I have aligned the channels to show Titan, but now Dione doesn't look right!

Now, I've manually cut out Dione from each channel and aligned them, leaving these colored blotches where Dione once was.

Finally, I used a brush to remove the leftover gaps in the channels created when I aligned Dione, and I darkened the photo to make it look sharper.

As you can see, if we want to compose a color image that shows Titan and Dione as they would have looked as Cassini was flying past them, we have to edit the photo in this manner. There is no way around it.