Cloud storage of non encrypted files and anonymity can not go hand in hand. You either encrypt the files very well before uploading them or, preferably, you do not store sensitive information on a server owned by a stranger. Leaks, hacks and every thing negative happened in the past, why put yourself under the risk of becoming only another additional victim to such event?
Not to mention you can not be anonymous if personal information sits in their cloud. Sure, I can store a file named 'tonynewham', it does not necessarily mean I am 'tonynewham', but one may immediately assume that I am!
Sensitive data need to be stored offline, not online so Cloud is not recommended for storing such sensitive data, even you encrypt it or not.
I understand that you meant if a user thinks that sensitive data file was encrypted well enough, it can be less risky for Cloud storage, but if it is paranoid security concern, avoiding Cloud storage is better choice.
With sensitive data, the advice always is never storing it online and on third party service such as Cloud storage companies and their data bases.