Well, shortcuts actually are files, and they're what CCleaner is trying to remove in my case. Here, I'll brake the issue down precisely--it comes about like this:
I install some software. I don't use it much, so I hide the shortcut in my Start Menu for the rare occasion I really need it.
Later I decide to just uninstall it, but--maybe I rearranged the Start Menu, maybe there's an oversight in the uninstaller--it doesn't get the shortcut.
I run the CCleaner Issue Scanner and the File Integrity > Start Menu Shortcuts scan identifies the problem "Missing Shortcut reference," data "C:\Documents and Settings\All Users\Start Menu\Programs\Example.lnk. Solution: Delete the shortcut file."
Attempting to fix the issue results in "Error fixing file issue (1). File: [C:\Documents and Settings\All Users\Start Menu\Programs\Example.lnk] File not found."
Now, if I change the Hidden attribute on that file, CCleaner finds and deletes it just fine. So the problem, apparently, is that CCleaner scans hidden files but fails for some reason to manipulate them. Knowing, thus, precisely where the bug resides, I could imagine it being fairly easy to fix.