Sorry, but that's not helpful at all and does not shed any light on your situation.
I respect that you don't want to reveal that link, but without actually seeing the output then I doubt you'll directly find a solution here.
The only advice I can give you is
1. Use TWO seperate browsers for testing. For example: use Firefox to log in change settings. At the same time use Opera, Safari, or even Internet Explorer to access the blog WITHOUT SIGNING IN. This way that second browser will get the output that regular viewers see.
Check the HTML source from that second not logged in browser.
2. Make sure you have fancy permalinks turned on. If you are using the default permalinks of ?p=123 then I don't think it will work. Edit: I see that you are using fancy links.
3. Switch to the default theme. Make sure that the default theme is not modified. Check with that second not logged in browser: does that show the correct WP-Super-Cache output in the HTML source? If it does, your theme may somehow be at fault.
4. Turn off all your plugins except WP-Super-Cache. I do mean ALL of them. Does that resolve the problem? If it does, turn them on one at a time until you find the culprit.