That hard evidence is not actually that hard. It doesn't have any weight behind the idea of who committed the act using the IP address. Consider this scenario;
A teenager, Bob, downloads a few albums off the web. Bob's dad, John, is the account holder with the ISP. When lawyers go poaching and tell John's ISP that xyz IP address was used to download copyright content, the ISP gives them John's details. After getting a letter from the lawyers, John, denies downloading the content. Because he didn't. Or maybe the letter asks John who was downloaded the material x months ago at 20:32. John says "How tf am I supposed to know?" - maybe he has a few kids. Maybe he has a wireless network that isn't properly secured. Maybe the time in question is so long ago that it's unreasonable for John to know who was using what.
Saying an IP address downloaded something illegally is one thing. Pinning the crime onto an actual person is a very big leap and leaves lots of room for reasonable doubt imo. I'd love to hear of one of these cases going to court and someone tries the "I'm sorry, but I don't know who was using the computer then" defence.