[djoldman]

I think this makes sense if specifically meant "only" but it doesn't. It means "exact":

  Specifically: in a way that is exact and clear; precisely.

The story can specifically refer to multiple people. There is no definite error here as I see it.

[dane-pgp]

The word "specifically" can also be used as an antonym of "generally", meaning "by most people, or to most people".[0] If a story applies to most people, but someone reading the story doesn't consider that possibility, then they have made a small error.

[0] https://dictionary.cambridge.org/dictionary/english/generall...