This is a side-effect of the way the TD is packaged. I'll add this to the FAQ.
If you want to insert your own images into your layout, you should either a) specify the image using a full, absolute path name; or b) place your image somewhere else besides the "images" folder of the Tournament Director install location.
So, for example (and using your example Captn), you could create a folder "graphics" and move the "background.jpg" image from the "images" folder to the "graphics" folder, and then reference it using:
<img src="graphics/background.jpg" border="0">
... or, you could leave it where it is and use the full path:
<img src="C:/Program Files/The Tournament Director 2.0/images/background.jpg" border="0">
Either of those should work. Notice that if you use the "Insert Image" button on the Cell dialog, it always inserts the image using the full-path. However, there are times when you might not want to do this (making the paths relative makes your layouts and supporting files more easily transferable to other users), so I would just suggest not using the "images" folder.