Having followed the development of the three strikes law since its inception, I am amazed that this person wasn't aware of the penalties involved given the sheer amount of publicity involved and are nothing short of gobsmacked that this person then continued to infringe copyright after receiving multiple warnings.
Maybe I am being more than a little harsh and credit where credit is due, the individual did write to the Tribunal explaining that they'd not been able to shut their torrent client down (yes it runs minimised in the system tray). The person then went on to say that "When this song was downloaded to my computer, a whole uTorrent program downloaded onto my computer..When I turned my computer on it said that the song was still downloading and maybe that caused the song to register twice as it being downloaded?".
Even though the Tribunal pretty much had what was a full confession, there was still not enough evidence hence the relatively small fine of $616 (which still makes the three downloaded tracks amongst the most costly music in New Zealand).
The really crazy thing is that obtaining music cheaply (or even freely) without infringing copyright isn't terribly difficult. According to RIANZ "A $616 fine delivered by the Copyright Tribunal would have bought the un-named file-sharing offender access to 20 million tracks on Spotify for four years". Free services such as YouTube and Pandora also stream music and music can also be downloaded from freemusicarchive.org.
Sadly this disciplinarian approach is what we're now left with. By now most tech savvy people have discovered legit sources for music and possibly also work arounds (such as seedboxes and proxies) to evade detection and prosecution. Sadly those less in the know are being hit hard, paying 200 times the value of the music they downloaded. Perhaps now might be a good time for RIANZ as the music industry representative to run a campaign promoting both free and commercial legitimate music sources instead of resorting to slapping the ignorant with a wet bus ticket.