Eh yes and no. Usually a representative of the rightsholder will join the swarm of a torrent, note all the IP addresses, and send their love letters to every ISP on that list. From there, the ISPs will forward the letters and may take action depending on jurisdiction and local law, which usually amounts to soft threats or suspending your account after multiple interactions. It isn't that the ISPs are spying on your traffic (at least in this instance), they just don't want to get caught up in "enabling piracy" or whatever nonsense. Hence why VPNs are a thing.