PreCheck can be given two separate ways - one is via the the public program (what you do when you enroll) the other is via the airline basically saying "yeah, this person is frequent enough that we don't think they are a problem" or they are traveling with someone who doesn't trip any of our flags.

There is a cost that the airline takes (I've never heard exactly what it is) for each person they refer to the TSA as pre-cleared, which I assume means there is a separate lookup against TSA lists, etc. It's at the discretion of the carrier. United does it all the time, Delta somewhat, and Southwest almost never in my experience.

So: a) Airlines can suggest pre-clearing you. b) There is some sort of match that the TSA also does. c) But just spend the money and get the full list.

Almost all security is doctrine and kabuki theater. 9/11's big problem wasn't security screening, it was that the doctrine of hijackings at that point was that the threat was hostages and negotiation, and therefore the best thing to do was to comply with hijacker demands.