I'm also a permanent resident with Global Entry. At least about a year ago, it seemed that non-US citizens can only get pre-check through airline status. Not sure about the current situation now that they started to give pre-check to random pax with no status.
My experience: I used to get pre-check through UA status, then it suddenly stopped when I got approved for Global Entry and put my pass ID (known traveler #) into my profile. I started to get pre-check again only after I removed the number.