The question http://superuser.com/questions/540289/online-backup-services-that-cannot-access-your-data is not my question and was closed by a moderator but I feel that the question is useful enough to fall in to the "allowable software recommendations" category. It is not just "I want software that does X" it actually is looking for an explanation on why or why not services offer backups like he is describing.

I put a answer in to a comment and would go in to more detail in my answer if I was not restricted to comment length and formatting restrictions.