The graduated response for anti-piracy laws is not a perfect law, but it is better than the stories you hear about a twelve year old girl being sued for hundreds of thousands of dollars for downloading music, unbeknown to her parents. Graduated response give the person a change to rethink their piracy without the heavy financial burden of no tolerance.
If you are paying for a service such as the Internet, that company shouldn't restrict you for your activities. It shouldn't even be monitoring your activities that closely to begin with. Also, another person could use your computer and download pirated material without your knowledge. Additionally, downloading torrents itself isn't illegal, downloading copy written material is. Downloading the copy written material may simply be a mistake, or they may own the material and are just acquiring it for a backup copy.