Say someone got your ISP's account details, and does something illegal (such as uploading some copyrighted material). Your ISP notices & contacts some media rights group as part of a request, & said group contacts your local Police. You haven't done anything wrong, but someone in your household has a BitTorrent client that they use for downloading/uploading
legal & uncopyrighted content. In the eyes of the Police, ISP, & court, there's evidence linking you & them to the crime (although you're not responsible), and you (the bill payer) is fined $$$ for something you aren't responsible for. —
cybermonkey 14 mins ago