Al,
Did your students see the whole webpage, and still not see the whole made up of the other parts, or did they only see your final creation? If all they ever saw was the final image, I'm not really surprised that they didn't figure it out because it is very well done.
If they saw the other photos and didn't start wondering about how that final image was photographed, hmmm... Maybe those students would like to buy an Arizona jackalope -- part jack rabbit with the antlers of an antelope (in case you've never seen them in your biology textbooks).
"Seeing is believing" has never been always true, and in this age, it's good that your students are being taught that lesson.
As for clients, there are still many people who have avoided computers and the wonders they can produce -- when an uninitiated person sees any improvement in an image that didn't require a trip to a photo lab, they are astonished. I love to see that look of wonder

..., but then have to admit that the computer program did some of the work.