Edit for clarity, since I'm getting downvoted: My point is that the analogy is not great. You can judge one person for their actions directly towards you. It isn't necessarily reasonable to judge a large number of people by the actions of a single person or small subset of the group, especially when the actions of the NYT are not directed at you specifically, which is pretty different to someone spitting on you.
You're right that the NYT has a lot of employees. If this were one guy writing a bad review, and the NYT took some disciplinary action against him, wrote a retraction and wrote a new article, then I wouldn't hold it against the NYT and I would probably increase my respect for them. They had a problem, employee did bad work, and they corrected it - that's good.
Instead, they just stood by the bad work and kept on without doing fixing the core issue. "It's just one person" doesn't really make sense because it's actually the whole organization not correcting problems originally caused by one person.
Put another way, if they're willing to lie and district to get a more sensational car review, what else are they willing to lie about? Who knows, perhaps they'll lie about some country having weapons of mass destruction to help trick the country into a pointless war. Okay, maybe that's a bit extreme - obviously they'd have to be extremely far gone to do anything like that.
But regardless of that, the decision to not apologize and admit they lied was an editorial one. It was their choice to die on this hill.
I'm just saying that the analogy to an (offensive) action by a specific person, toward a specific person, is a poor analogy for the actions of some subset of a large organisation, which almost certainly isn't directed at a specific person.
And I doubt many people would equate the actions of the NYT with literally being spat on.
There is a difference between making a mistake or being wrong while trying to be right, and intentionally doing something bad or refusing to acknowledge error. Everyone is in the first category sometimes, but you don't really have to be in the latter category.
If the NYT is intentionally doing bad things, even once or a handful of times, then I don't think it makes sense to forgive and forget until they show me they understand and have corrected the issue.
The problem is that for most things I can't tell if they're right or wrong or arguing in good faith or not. If something comes up where I can definitively tell, and they are definitely acting wrong - it destroys lots of credibility because that's really one of my rare chances to evaluate their performance. I can't trust them in domains I don't know about if they aren't very good in domains I do know about.