I believe your understanding is perfectly correct Questioner37, however you would find that you need to re-install the entire Adobe CS6 as you cannot isolate just one software from the suite.
What i did was uninstall/delete only illustrator from my computer then initiate the entire suite reinstall to isolate illustrator. If you choose only illlustrator from the cloud download, you would get an empty shell software file.
What i would like to pass on is, best to reinstall the entire suite without isolation, that way one does not tinker with the original packaging of Adobe CS6 suite.
Hopefully this explanation will make sense to you, if not now, when you get to doing it.