The sentence spoken at the Council of Elrond is precisely:
The Nine the Nazgūl keep.
Given the many other passages by Tolkien in which Sauron himself possesses the Nine, it would seem that Tolkien, as he often does, is using inversion here. The sentence has “The Nine” as its subject. What do “the Nine” do? They “keep”. What then do the nine Rings keep? They keep the Nazgūl in line for Sauron.
The sentence would be translated into normal modern word order as “The Nine keep the Nazgūl.”
Christopher Tolkien unfortunately does not cover Gandalf’s explanation in the HoME volumes, as least so far as I have found. So HoME sheds no light on this sentence.
That is the only explanation that I have discovered. I read this suggestion years ago in some fanzine. Tolkien, more used to including inversions in the words of his speakers then most modern readers, might not have noticed that this sentence is ambiguous, especially since he would already know what he meant by it.