If the blade is held at any fixed angle relative to the stone it will only contact the edge and the spine in one spot. The edge and the spine of a smiling razor lie on a conical section. The conical section is flat enough that it is hard to recognize it as such, but it is. In order to contact all of the conical section it has to be rolled.
Take a dinner plate and lift one side until a spot near the outer diameter touches the table. It will only be touching the table in two spots one near the outer edge and one on the ring on the bottom of the plate. Do you see how you have to roll the plate to get other spots to contact the table? A smiling blade is the same but on a small enough scale that the roll is very subtle.
One of the best explanations I've read!
I've never understood the 'X' as it's more of a 'C' as you have described very well. :