I feel this is dealt with by the fact that law has a concept intention. Handing out the recipe for reconstructing the pirated material counts as aiding piracy, I would say.
Granted, the fingerprinting algorithm used by YouTube is pretty good: http://www.csh.rit.edu/~parallax/
As an, albeit somewhat contrived, example:
Let's say I have a music player on my computer that, when fed the works of Shakespeare, it plays the Gaga's latest hit and when fed with the works of Sir Arthur Conan Doyle, it plays Jingle Bells.
My actual intent is to read Shakespeare and to listen to Jingle Bells, but that is going to be a pretty difficult case to prove in a real court of law. The assumption will be made that I had the player and copy of Shakespeare so that I could listen to Gaga.
Theoretically, unless Shakespeare has been interpreted by said program, I have not committed any crime. But precedence disagrees. Just having the right sequence of bits on your computer is enough to prove intent, whether your actual intention was to use it to violate copyright or not. That is where I get lost.