Well its a subjective question, since "how" private do you want your server to be ??

Private is something which you can only access, but it also means in otherway, stuff that you only has access too..

Yes, you can create a server and disable every other possible form of log in, hence without your root access and IP, you only can access the VPS unless you plan to grant access to others.

But this data is stored in DO premises and within certain country specific jurisdiction so theoretically acting on court notice (if any court does so) DO may hand over the data to respective authority..

;)