The claim is for a downloading fee, not for distributing it, as I read it. If their Sky account says that they will pay when a film is downloaded, then they owe Sky, as a film was downloaded, even if it was the neighbours what did it. If the Sky account was either in the free trial period, or included free downloading of movies, fine, but I don't see either of those explained in the original post. If one of those conditions was true, then I would agree with you, but not if neither one was.
If my neighbour siphons off my electricity supply without my knowing, I, as the account owner, still owe SSE for the bill. It is then up to me to regain the value of the stolen power from the neighbour.