Yes - it is confusing. My understanding is that PreCheck is a screening process that is available to travelers through a number of methods.

First, some frequent fliers are able to request PreCheck from an airline where they have status. Once requested, they can be granted access to PreCheck by TSA through the airline with whom they have status.

Second, one can gain access to PreCheck if one in enrolled in a Trusted Traveler Program (GE, Nexus, Sentri). If one is enrolled, one can enter that TT information into their profile with airlines. In this case, one can enroll with any airline that will accept entry on their TT data. And, given that, they can qualify for PreCheck with airlines even if they do not hold status with that airline.

In my case, I cleared PreCheck with AA because I was Platinum. I also enrolled in GE and have entered that data into my FF profile with a number of other airlines which qualifies me for PreCheck if I am flying other airlines and there is PreCheck available at the airport.

I think that is an accurate summary. If anyone has any more info, interested in hearing it.