I'm mad. I was just on the phone with Adobe technical support, I think the guy's name was Avanish or something like that.
My Creative Cloud app was showing updates to Premiere CS6, which is not installed, and he said I can fix that by uninstalling and reinstalling Creative Cloud Desktop, without uninstalling any of the other applications. So I clicked the uninstaller he specified, and ALL MY CC APPLICATIONS ARE GONE.
This is going to waste several hours downloading many gigabytes of installers.
And worse, when I reinstalled Creative Cloud from the website, it still thinks my apps are installed, so it doesn't show the download button for any of them. Now I have to figure out how to trash its preferences.
Upate: Creative Cloud Cleaner tool made it pretty easy to start fresh, but this is still very frustrating!