I cleared cache, but no joy.
I looked in the Drupal Answer you referenced, the solution for which was to upgrade to Drupal 7.21. My install is up to 7.22, so I'll keep digging.
From my XML file, I see that
part="image" is referenced in this location:
This one displays when hovering over the broken image icon and when you enter it directly into a browser.
and part="thumbnail" is:
This one gets the Denied access message when you enter it directly into a browser.
and part="original" is:
This one gets the Page not found message when you enter it directly into a browser.
I verified that the thumbnail and original settings were actually saved in the Image Asset display control.