I really want to change the icon that is associated with a document!
I just found this while searching for the answer to this same problem with Skype,
The default desktop Skype icon represents the so called Advertised Shortcut. This is a special type of shortcuts which actually don’t point to the program executable but to the program installer which on startup performs check of the program’s integrity. See here for a better description:
Actually there are several other programs using this kind of shortcuts, e.g. Microsoft Office programs.
If you want to have the ability to change the icon then you can just create your own Skype.exe shortcut.