The Denny Crane character has a Gulfstream, and he's mentioned that more than once. So why is he flying commercial and putting up with the hassle?
He doesn't seem like the type of guy who gives a rat's ... about
frequent flyer miles.

On the episode, he was denied boarding while attempting to fly
from Boston to Hawaii with his former fiance (the little person's mother,
played by actress Delta Burke). The incident at the airport is talked
about but not actually shown.