The question https://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.