Not to start a linguistic rabbit hole but the correct analogy would be "a certain language and social dialect tend to produce stories with a certain theme and dialog".

>Ridiculous and provably false.

If you prefer a counterexample, a couple of years ago I noticed that Apex Legends was a Source engine game without external info, and that Source version is heavily modified. Of course one can modify the provided defaults to a point that even the most no-life individual couldn't guess the engine.

I watched a cool video about the whole "engine grain" thing recently with more examples. https://youtu.be/SOwYqwsEdXc