It’s not just torrenting. Every user chooses what files they share, and these would be visible in search (and ranked by an internet speed transfer estimate), which makes discoverability a whole lot easier. If you want to download it, a direct transfer is initiated between that user and you computer only. You can also browse all files that a user has shared and chat with them about problems and whatnot (there also are chat rooms). Plus, since it’s not really torrenting apart from the concept, your download history isn’t targeted by popular tools that check out your activity on public trackers.
I think you’re confused. There is no warning letter, that’s just the takedown notice sent at the same time as the takedown.