I finally understand the DisplayPort situation, thanks to your post here:
Your explanation was simple and thorough, so I'll quote it here for those in need:
"DVI and HDMI signals require timing signals generated by internal clocks on the card. DVI and HDMI displays need timing signals to display the picture. DisplayPort capable displays do not need timing signals. To save space, cost and complexitiy there are two internal timing signal generators in the ASIC of the AMD ATI Radeon HD 5000 series. This limits the number of outputs with timing signals to two. To enable the third display, you must use the card's DisplayPort connector. If you use an adapter to convert DisplayPort into DVI or HDMI, you must add the timing signals to the output, too. This is done by using an active DisplayPort adapter."
Thanks again for explaining the hardware design and its impact...