If they didn't have evidence from the ISP you wouldn't have the letter....
It's been said a hundred times before unlike a criminal case they don;t have to prove you guilty beyond any doubt, all they have to do is show thier evidence and unless you have evidence to the contrary then they win
It's mentioned recently that the unsecured network defence is working great in Europe... I suppose then that even if it doesn;t work here the European court of appeals would be the place to go