NYT is a publicly traded company. Their first responsibility is to their shareholders, not "the truth".

It’s not that black and white. Over the long term, shareholders are better off if the journal can maintain a reputation of impartiality, so it would be difficult to prove mismanagement in this case. It’s like when Apple cared more about customer satisfaction and doing the right thing than short-term ROI. Sure, shareholder could sue, but they would likely lose.

The idea that a company must only do what brings shareholder money immediately is a meme that is widely propagated by a certain class of people who stand to profit from it, but the law does not impose that behaviour.