[Elladan and Elrohir]

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?

I'm not saying he doesn't; I just can't recall if he does or not.

That's point one for believing Gandalf.

Point two: Tolkien responded to a critical remark about some of Treebeard's statements by saying (and sorry, I must paraphrase), Treebeard is very old and very knowledgeable, but "he is not one of the Wise" (direct quote) and there's a lot he doesn't understand.

Gandalf, on the other hand, is unquestionably one of the Wise; the implication is that we can trust statements about things like Nazgul if one of the Wise makes them.

So those are grounds for believing Gandalf's unequivocal statement.

Having said all that, I do indeed believe that Gandalf's statement is merely a leftover mistake by Tolkien: he states multiple times in UT and the Letters and implies elsewhere that Sauron keeps the Nine Rings.

Of course, neither the Letters nor the UT are "canonical"; I believe most Tolkien geeks would agree. So I suppose it comes down to whether you're a strict constructionist, going totally by what Tolkien approved for publication, or more of a liberal.