[Morwen]

It is of course a mistake by Tolkien, probably a mistake in his writing Gandalf's words at the Council.

But I suppose, technically, if you're going by canon, you would have to say that the Nazgul possess their Rings. "The Nine the Nazgul keep" is not an inverted thought; it is a clear statement from Gandalf, and the context shows his meaning.

Could Gandalf be mistaken? Of course; who cannot? But, I'll just ask the question and open myself up: Is Gandalf ever shown to be mistaken about anything in the text? There are things he's unsure about, definitely. But is he ever wrong? He may doubt whether something is X or Y (e.g., not knowing the identity of Durin's Bane), but does he say something is X when it's really Y?

The problem though is that the contradiction exists within the canon.

So it is now: the Nine he has gathered to himself; the Seven also, or else they are destroyed.
Gandalf to Frodo - The Shadow of the Past, FotR

However, Gandalf later states,

Yet it is a ring. What then? The Nine the Nazgul keep. The Seven are taken or destroyed.

The Council of Elrond, FotR

I agree that "The Nine the Nazgul keep" is not an inverted thought. Gandalf is making a statement about the possession/location of the Rings of Power. However he appears to have changed his mind as to who actually holds the Nine. If there are sources outside of the canon which support the first statement, i.e. that Sauron holds the Nine, then I think it should be preferred to Gandalf's later pronouncement.