I'm probably in the minority here, but I feel like the biggest failure in all of this wasn't Musk's response, or the incompetence of the NYT's reporter, but the "support" Broder received over the phone.
The extraordinary event in the original NYT article was that the car "died" during Broder's review. We can debate all we want about the smaller facts in the article, but if the car didn't die during the review, we probably wouldn't even be discussing the article today.
To me, the most glaring issue that came out of the article wasn't a problem with the car. It was clear to me as the reader that Broder was trying to push the mileage limits of the car. But I personally think the car would not have died if the people on the other side of the phone had simply given better advice.
At the very least, Musk should consider retraining (or replacing) the people he allows on the other side of support calls with members of the media. It's better to give inconvenient advice (i.e. "charge it a little longer just to be safe") than give advice that risks getting the driver stranded.
The key decision the reporter made, and that NYT ombudsman acknowledges was bad judgment, was to quit charging early in Norwich without being given the go ahead by Tesla.
The reporter changed his wording on that between the original article and his later rebuttal. He originally said Tesla told him it was okay to unplug and go. Later he reworded that they'd told him it should be okay to charge for an hour and go. He then charged for less than an hour, saw it hadn't given as much fuel as he needed, and unplugged early anyway and without checking with them.
As the NYT ombudsman quote, the journo hadn't even bothered to follow the owner's manual. His behavior was disingenuous at best, even if not pro-oil link baiting at worst.