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][1]" 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.

  [1]: https://meta.superuser.com/questions/5372/how-do-i-ask-a-question-that-may-require-recommending-software