All the rights-owner has in an IP address and a time (plus what was being shared). All Verizon have is that the IP address was assigned to your connection at that time.
The US legal system is weighted in favour of those with heaps of money/power/both and is also a bit more draconian than in Western Europe or Australia but I'm fairly confident that they would still have to prove that it was you and not a family member / housemate / person in a car in the street stealing your wifi, who was responsible for breaching their copyright. Companies have also been know to bully/frighten people by telling them that they could be liable for fines of up to a bajillion dollars, but they'll settle quietly for only - how much do you have in your account? - $7,500 it is then.
Just to clarify, they almost certainly have not pinged you for downloading a vid - the only way they could know that is if they had access to the server from where you got it, or your end-device, or they're the NSA and have compromised one of the routers that your traffic passed thru.
No, what you have prob been done for is sharing the vid with other torrent users. If you configure your torrent client to not share your stuff with others, you're practically invisible, and can download with impunity.
Just to be clear, I don't support piracy unless it's on the orders of the King.
And it's the 18th century.
