What law is this exactly? I've done a quick web search, but couldn't find anything describing quite this. Most sources suggested the law outlaws distributing (i.e. uploading) copywritten material, not downloading. This seems like it would be similar to US law...

Maybe I should have mentioned the threat of criminal charges, or defined piracy as downloading (but it seems like you understood it this way too as you mentioned "downloading a public torrent"). Rights holders do make sure there are news stories every so often about lawsuits around some act related to piracy, but of course regular people can be bullied in the courts, whether they are truly liable or not.