Reading between the lines, one can deduce how this particular automated check probably works.
The automated check would first check the person's nationality against a pre-defined list of English-speaking countries. If there's a match, the automated check passes. I would expect that these countries would be Australia, Canada, Ireland, the United Kingdom and the United States (this would be consistent with INZ's definition for the Skilled Migrant Category, per
SM4.5).
If there isn't a match, the automated check would check the person's visa history, to determine whether the person held a visa for which English proficiency is a requirement (the Skilled Migrant Category Resident Visa is an obvious one). If the person held such a visa, the automated check passes (because, if one didn't have sufficient English profiency, one would not have been granted said visa).
If there still isn't a match (e.g. an Indian national who gained residency via the partnership pathway), then it would be necessary to check the person's supporting evidence of English proficiency submitted with the citizenship application, and that would require a manual check.
Of course, I have absolutely no idea how this automated check actually works, but I believe this to be a reasonable assumption.