Full link doesn't affect - I've tried it. Funny thing about this case, is that if I copy an image location from Google or any other website - it shows the custom image. However, it doesn't show any images I have uploaded to media library. I checked that I can see the image with straight image link.
However some images I can't see with direct link and I'll get:
You don't have permission to access /XXXX/wp-content/uploads/2012/06/noweb.jpg on this server.
Folder permissions are 755 so that should be enough. If I use those images in articles, they are shown correctly. I wonder if this is a problem with server permissions, but that doesn't explain why I can see some uploaded pics with direct address and some of them I can't :/