I'm currently midway through watching a box set of a British sitcom called Hi-de-Hi!. It's about a holiday camp in the late-50s/early-60s, and was originally shown between 1980 and 1988. By a strange coincidence, less than 24 hours after Roger's review, the episode I'm watching has another reference to that scene in "It Happened One Night". When two staff members have to share a room, one of the others says, "Did you ever see that film with Clark Gable and Claudette Colbert where they have to spend the night in the same room?". Another person then names the movie.
The episode of Hi-de-Hi originally aired about a year before 'Close Call for Daisy', so maybe "It Happened One Night" was popular amongst script writers in the 1980s (on both sides of the Atlantic).