That's right. Letters to the editor which "correct" the New York Times editorial writers, or contend that the editorial was in fact "wrong" cannot be printed as a letter to the editor.
That would be the New York Times editorial page policy.
If you are looking for a laugharoo, Eugene Volokh has a fun little story on it here.
The Times responded: “We cannot say ‘incorrectly’ because that is the province of corrections, in which case I would forward the letter to the corrections editor and it could not be considered as a letter."Your letter which corrected our editorial cannot be considered a letter.
What we always suspected.