all they need to know is the ip address. It doesn't matter who the person was, if it came from that ip, the person that pays for service that had that IP address is responsible. This seemed to work accurately with comcast, I see no reason why Verizon would be any different.
I will disagree with you on that point. Lets assume someone steals my car and it's used in bank robbery, am i responsible for it because it was my car?
Now lets use same analogy but this time with the router. I use wep security(cheap lock) because well i don't knowany better. Someone cracked that lock and used my router for illegal activity. Should i be accountable for someone else action that used my router ?