Honestly, this just seems like nitpicking. Your main complaint about their email is that their apology isn't phrased in the vernacular? Don't we have better things to do with our time than complain about things like this?
I'm sure many people would think that the New York Times speaking to them in a conversational tone is inappropriate and unprofessional.
A big difference to whom? I don't think the author intended to imply something different by using that particular language.
I doubt the author consciously thought: "i'm going to make this apology less effective," so who cares if the language didn't exactly resonate with you or the OP? I don't think it was malicious or disingenuous; if anything, the NYT needs to hire better copywriters, so their emails don't get dissected as frequently.
I'm sure many people would think that the New York Times speaking to them in a conversational tone is inappropriate and unprofessional.