Doesn't not understanding syntax get you in trouble? Yes.

Over at the NYT a commenter questions Dick Cavett's English:

For one so usually careful about English usage, I am surprised to see Mr. Cavett using the double negative in the third paragraph of the press conference/gutsy reporter portion of his article.

Shouldn’t it have read “Never announcing a date allows them to return . .” rather than the awkward “Doesn’t never announcing . . .”, equivalent to saying “Does not never”?

Can Cavett really defend using “Doesn’t never”?

Well, I'm sure Cavett can. Whether he will or not I don't know. But this is a perfect example of an incorrection, that is, a "correction" which is wrong. (Let's not even mention the commenter's own misplaced "dangler" - "for one so usually careful" is presumably meant to apply to Cavett, yet as written it applies to "I".)

This sentence is a simple question: Doesn't X do Y? The suggested correction changes the question to a statement: X does Y. Now, Cavett clearly meant his rhetorical question to be answered "Yes", but he wanted the readers to do it, not himself. The whole force and structure of his argument suffers if he states instead of questions.

Moreover, for this to be a double negative, as the term is used in these contexts, the "does not never" would have to be one verb phrase, as in "He doesn't never write well." But clearly, the "not" and the "never" are not both modifying "does". The "does" isn't providing the do-support of questions & negations to "announcing" - the ING form never has do support (it's always used, as a verb, with the auxillaries "be" and "have" and do support is only done when no auxillary is present. You don't say "he does not be announcing" or "he does not have announced", not in Standard you don't. The do-support is going to "allow".

In other words, the X of the question isn't "announcing"; it's "never announcing". And the question is "doesn't X allow?"

Two separate verb-like clauses (announcing a date; allow them to return) are present, and each has negation. The "not" and the "never" are each modifying a different verb - "does not" and "never announcing" (oh, all right, "annoucing" is only a verbal; call it a gerund or a participle or whatever you like, the never still goes with it, and not with "does"; it's verbal enough to have its own object (a date) as well as its own adverb). That makes this structure not only legitimate, but effective.