I wouldn’t be even a tenth surprised to find out that the name of the later-made TV show was designed as a partial homage to that exact episode that preceded it.

Though maybe not, as the concept seems to describe something deep in our psyches, and appears in so many shows & songs (e.g. R.E.M.'s shiny happy people), and I would bet that the Twilight Zone episode itself was either based on or at least was was preceded by some ancient story written or told hundreds of years before it:-).