I had similar idea a while ago, although it didn't involve bitcoins and I never actually acted on it.
How do you solve the problem of an evil storage node provider who detects that you're trying to recover a file from backup, blocks it and sends you a "transfer X BTC to my account to get your data back" email?
How do you solve the problem of an evil storage node provider who detects that you're trying to recover a file from backup, blocks it and sends you a "transfer X BTC to my account to get your data back" email?