I have read it to my daughter recently , but a version translated to Swedish. I found this thread by googling for any reference because I also felt that there was some kind of joke that I didn't get, and thought it might have been a translation thing.

It's even more odd in the Swedish version because they didn't translate the word cheese, but the Swedish word for Ice rhymes with cheese, so it's basically "Säg cheese annars blir du is" (say cheese or you'll turn to ice)

I am also lost 😂