I don't think it's the ISP monitoring for torrent traffic, but copyright holders honeypotting torrents and keeping track of the IP of seeders, maybe leechers too I guess. If the IP holder isn't on the tracker they don't see that you're pirating their stuff.
Private tracker's "business model" as it were relies on a central tracker tracking the download and upload ratio of your client. They explicitly disable DHT as it misses the point of the economy.
The ISP in general isn’t going looking for your torrent traffic. The DMCA groups are, and when they find it, they contact your ISP to enforce it. If it’s a private tracker, there’s a decent chance the DMCA groups’ tracking bots aren’t able to see that traffic.
Aren't some ISP in the US owned by media companies? For those there would be a clear incentive to scan their customer's traffic for copyright violations, right?
Yes as the above commenters say the copyright holders (their enforcers really) don't have access to the private trackers swarm and will be unable to report your IP address.
It requires time and effort though.