Reasonable doubt. Google it. Many network based exploits are hard to to initiate but the fact they exist make it a possibility. You must be a noob NOC tech if you think only a super spy is capable of hacking an ISP's router and controlling the routing of a block of IP addresses. How do you think hackers/bots/etc.. hide their tracks?? Just because you think "your" network is secure doesn't mean the upstream provider's network is.
You don't log in to an IP. That doesn't make any sense.
Your modem is assigned a DHCP address based on its MAC address, which can be easily forged or spoofed. And so can IP addresses. How do you know a hacker hasn't compromised an ISP's edge router somewhere and has hijacked your IP address?? Or that the kid across the street hasn't cracked your WEP or WPA protected wifi?? Too many ifs to bring someone to court.
Bottom line is they would need more then an IP address. Show me the packet captures of the "alleged" copyrighted material that was downloaded to my ip address.