You mis-paraphrased the argument. Your paraphrase insertion [] is incorrect. It should be: [that such x-ist labels are applied to statements regardless of thei

You mis-paraphrased the argument. Your paraphrase insertion [] is incorrect. It should be: [that such x-ist labels are applied to statements regardless of their truth or falsity] Your conclusion is roughly his point, but his point holds independently of the "truth" of the underlying statement.