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Setting media/skin urls to another domain breaks image uploader in wysiwyg editor

If I set the "Base skin URL" and " Base media URL" to a domain other than the one used for the "Base URL" the image uploader in the WYSIWYG editor breaks.

The "Media storage" popup appears and I can select an image using the "Browse files..." button but any file I select isn't shown in the list and the " Upload files" button does nothing what so ever.

I already checked the JavaScript console and the access/error logs of my server but nothing seems to happen at all.

How can I fix this? Or is this a 'feature' and do I have to disable my custom/cdn URL settings just to be able to upload a new image?