It is not related to the cabin you are booked into.
Not sure about that part. I've been Medallion on Delta for over 10 years (at least silver, several years gold). Sometimes I get pre check, sometimes not, but it's near 100% when I'm in business/first, less than half when I'm in coach.
The real surprise (this was a few years ago) - I was traveling with my wife. Booked together on the same ticket, I'm Gold Medallion, she's only got a handful of miles on Delta. She's also a resident alien (Green Card), from a predominately Muslim country (although she's Christian). She got pre-check, I didn't
