Data on Storj is by default end-to-end encrypted with keys only the data owner controls (with optional support for sharing features). Only the data owner can decide who to share the keys with and who can see the data. Put another way, Storj can’t access data without the data owner sharing keys and access!
However, if the owner shares the encryption keys and provides access to others, it can be further distributed by others. Storj does not allow illegal content per our terms of use and conditions. If someone has stored potentially illegal content and shared it with others, law enforcement may seek to obtain information by way of a subpoena, warrant, or other legal process. As you probably know since you're reading this thread, often such inquiries are confidential and the recipients may be prohibited from disclosing their existence.
If you're interested in our encryption and security design decisions, there are a lot more details over at https://www.storj.io/disclosures. Glad you're all paying such detailed attention!