Take it for what it is (unsubstantiated), but it's my understanding from more than one senior Bethel contact that it's the GB's standard policy to only ever fly Coach/Economy, even to the point of refusing frequent flyer upgrades, lest some lowly J-dub see them comfortably tucked into First as they slog their way back to the cheap seats.
What was joked about when informed of this policy was that their wives aren't as recognizable, and therefore can get away with the free upgrades!