Most of the time all tile goes on the same surface. The design tile usually is put in place of the non design tile not on top of it. I put a link below to some pictures of my kitchen tile that I just put in. I took a close up that may help.
Most people I have talked to agree with you. However, in your examples, here, over a stove is a design put over the first layer of tile. It looks good to me?
Carol, you are correct, there are exceptions! It is rare though, being very dependent on the style and pulling it off. Different tile depths can create difference challenges too - cleaning for one, another is if the design is near any electrical outlets/switches.
Behind the cooktop I have often seen/designed tile framed out with a pencil or bullnose - so it may look deeper, but it is not. When I have put tile on tile is only with embellishments.
Hope this helps! What are you exactly thinking? Are you trying to work with what you have, or going all new?
I can't see any examples at the brightenelectric.net page. But Stuart's photos are of tiles that are set in between the background tiles, not on top. I saw a backsplash with accent tiles placed on top of the background and it just didn't look professional to me. The unfinished sides of the tile shows when placed on top. Go to a tile store and see how it is done. I would also be hard to clean around and perhaps be more likely to fall off.