The problem is as the law stands, you not only have to prove that you are not the person the did the illegal downloading (or uploading) from the IP address which they have tracked the download from (which in my opinion is usually planted there to attract people to begin with which I would also call enticement) now the main problem is that according to the powers that be (your IP), the person who's name the address is registered to is responsible for the usage of that line, so saying someone accessed it when you did not have a password on the wireless connection is that you did not make every attempt to secure the connection, therefore, guilty as indicated.
But back to the original problem, and that is that far too many of these money grabbing so-called lawyers have been sending out demands for money supposedly on behalf of a client to all and-sundry, even to people who have never used let alone owned a PC in there life.