Right. But what I meant by "I don't understand" was more along the lines of "So it's 11/11/11 again. Who cares? Oh, and by the way, every 11/11 is Veterans' Day..."
I don't think we need to read too deeply into the selection of the date. This is little more than a slice of trivia, the equivalent of saying "On this day, 100 years ago...". The choice of back-dated front page doesn't have any profound consequence, other than as a passing curiosity. I don't think the NYT is trying to make a statement with it.
First, Veterans' Day, by that name, was only recognized after WWII, as you say, but 11/11 was a day of remembrance long before that under other names (Armistice Day or Remembrance Day).[1]
Second, obviously a newspaper from 11/11/11 is earlier than a holiday on 11/11 precisely because the 11/11 dating comes from the end of World War I on November 11th, 1918 (on "the 11th hour of the 11th day of the 11th month"). I'm sorry if my point wasn't clear, but my original comment refers to World War I, 1918 and a poem about the start of World War I.
My original point remains: Today is (in many countries, not only the US) a national holiday in remembrance of the veterans of World War I or veterans more generally. I find it depressing that people care more about a piece of numerical trivia than that.