First of all, nothing's wrong
If you open Windows Explorer, browse to the following folder:
C:\Documents and Settings.
Here you see a couple folders:
-All users
-Administrator
plus a folder for each user.
If you open your own folder, you'll see a folder Desktop there.
All the icons for programs you use, are there (except the standard icons: My Computer, Internet Explorer, etc etc).
Now when you look in the Desktop folder under your name, it may be empty. But you still have all kinds of icons on your desktop, how is that possible?
Well open the folder C:\Documents and Settings\All users\Desktop
Here you see all the icons that are on everybody's desktop (including yours).
If someone would delete one of the icons, it would indeed affect all users (including yourself).
Now, how to prevent that.
If there are programs that you use, and you only, simply move the icon from:
C:\Documents and Settings\All users\Desktop
to
C:\Documents and Settings\*your name*\Desktop