Usually when you delete a file using the sharing folders window, then it is deleted from the Sharing Folders cache on your hard drive. If you delete it from the folder it is usually re-downloaded. (Although this makes the USN journal service have no point in my opinion...)
I think Nile may be right now I think about it - I think you are only able to delete your own files, not 100% on that... will do some testing... when I have a contact online