No, not necessarily. But maybe the answer to your question depends on the perspective of the one asking:
1)The writer
2)The producer (or whoever is in a position to “buy” the writing)
3)The eventual/prospective audience or reader
(and btw, are we limiting this to scripted work or any category of fiction writing?).
And is the “pitch” necessarily the same as the story? The pitch for Traffic might be “Looking at the drug trafficking trade from several different points of view.” but that really doesn’t tell you anything about any of the storylines, does it?
Your example would be considered a bad pitch, IMO. The pitch isn’t just the subject of the story, but an attempt to ecapsulate the concept (or “theme”, if you prefer) within the subject/story in both an original and interesting way.
I’d still assert that if the writer can’t do that in less than 3 sentences, odds are the script is either ill conceived or poorly executed. This doesn’t just speak to whether or not the story is good, but whether or not the writer has a firm grasp of the story itself. A good story can be poorly told (not sure if you want to consider that result a “bad” story or not).
**Well, I didn’t get this impression. That Wordplay column doesn’t mention anything about good or bad stories. But if you’re right, can you name a single movie with a bad story that can’t be described by one of Polti’s 36? It seems to me that they’re so broad they could apply to any story, not just good ones. **
Wordplay is a site for wannabe scriptwriters who want to sell their work. From that perspective, “good” equals “saleable” or “successful”. A writer (or prospective writer) can use Polti’s 36 (or another theory) as a guideline to that end. Doesn’t necessarily guarantee the end result will be “good”, because there is another factor involved - individual writing talent. Again, a good story can be poorly told.
In film or theatre, the story itself is just one facet of the final production - there are plenty of bad movies/plays - doesn’t mean the story was bad, does it?
And of course, there are always “exceptions to the rule”, or debatable exceptions. My earlier cite claims that Hamlet is an exception (as in, not considered to be a “standard” good story).
Which prompts me to ask for a distinction that might need answering before the OP can be addressed further: What is the criteria (in the OP) for a “good” v. “bad” story? Why is Hamlet considered a good story?