I think you missed the point of the story, which was that the company was asking for a combination of skills that never exist in the same person. An unicorn. In that context it is reasonable to assume that if you have the core competency (in this case design skills, not coding), then you should apply.

Also fizz buzz has nothing to do with the kind of programming that was expected from the job description. Now you might reasonably object that fizz buzz is supposed to be something so rudimentary that any programmer could implement. But the point is UI/UX people don't typically do any algorithms work at all. Their interaction with JS is often just to call an API and shove the resulting data where it needs to be in the DOM. They may never have to use a loop, ever. Or conditional testing. Or think about infinite sequences. To a proper software engineer like you or me fizz buzz seems ridiculously simple. But I could totally see a UX designer whose only interaction with self-taught JS is to glue APIs together being tripped up.