The error needs to be fixed. On the other hand, the New York Times’ mistake also needs to be a matter of public record. So the archive needs to, for integrity sake, make note of the original version as well as correct the error, lest someone be mistaken about the history. The correction should also be time stamped so that someone can tell just how long it was published incorrectly for.
It’s a good example of how bad reporting can spin history – which is often the point.