Using the SharePoint Web Service Copy.asmx, you may notice this message on copied items: This item is a copy of
What I was doing wrong was, I used the destination URL in place of the source URL. If you provide a source URL, you will also receive the This item is a copy of… message in the properties view of the item. To avoid the message all together I replaced the source URL with the file name.
//bad
cWs.CopyIntoItems(destination, destinationUrl, fields.ToArray(), myBinary, out result);
//good
cWs.CopyIntoItems(filename, destinationUrl, fields.ToArray(), myBinary, out result);