Subject-verb agreement - the applicable rule of grammar here - is not in dispute. The disagreement is whether none is singular, plural or indefinite. Figure out the etymology and usage of the word in various contexts, and the applicable rule of grammar that applies the corresponding verb form easily follows. Call the issue a grammatical one, if you must. But please don't dismiss the opinion of a highly respected editor, author and teacher simply because he subtitled one his books "A Modern Guide to English Usage" instead of "A Modern Guide to English Grammar." The same goes for The Cambridge Guide To English Usage. In addition to those references, I've also pointed you to The Oxford Dictionary's usage reference. If none of those suffice, consider what The American Heritage College Dictionary has to say about the matter:
"USAGE NOTE: It is widely asserted that none is equivalent to no one and hence requires a singular verb and singular pronoun: None of the prisoners was given his soup. But the word has been used as both a singular and a plural form from Old English onward, and the choice between a singular or plural verb depends on the desired effect. Either a singular or plural verb is acceptably used in a sentence such as None of the conspirators has (or have) been brought to trial. When none is modified by almost, it is difficult to avoid treating the word as a plural: Almost none of the officials were interviewed by the committee. And in sentences such as None but his most loyal supporters believe his story, none can only be plural."
Then there's Wikipedia classifying none as an indefinite pronoun with, both, singular and plural uses.
And last, but certainly not least, there's the video on Merriam-Webster.com addressing the Old English use of none as a plural, notwithstanding it's derivation from no one.
So, in summary, we can accept what Cambridge, Oxford, Merriam-Webster, Wikipedia, American Heritage, a noted The New York Times editor and usage expert and, no doubt, numerous other experts say about the matter or we can accept that NONE of them HAVE "thought it through" as carefully as you have.
A pretty stinging condemnation based on nothing more than a passing reference to a literary foil. Bernstein's own rejoinder says it better than anything I could offer:
"There is a perfectly legitimate code governing grammar, usage and style, but the code is set up neither by cranks nor by know-nothings. It derives from the generally accepted standards of educated users of the language, often but not always influenced by what the masses say. What the code does not need is ex cathedra injunctions by tinkerers who would tamper with idioms, invent grammatical rules and clamp word meanings into an everlasting vise. To resist them is almost as necessary as to resist those who maintain that whatever the people say is just fine. Both camps contribute to confusion and imprecision. What we require is neither a language that is cramped nor a language gone wild."
-- Miss Thistlebottom's Hobgoblins: A Careful Writers Guide to Taboos, Bugbears and Outmoded Rules of English Usage
