Image uploads not working with download method set to private?

Issue Summary

I tested Whizzywig on my local machine, and I liked it - seems to suit my needs better than the Wysiwig-module.
But the big disappointment came when I activated the module on my shared hosting account: images that I uploaded and inserted via the browser do not show up, neither in the edit-view nor in the saved node. I guess this has something to do with the download method: on my local machine, it is set to public, on my internet account it is set to private. The files that I uploaded with Whizzywig don't have entries in the "file"-table, might this be related?
Anything I can do to make it work?