There's also a big difference between "apologize for any inconvenience caused" and "for the inconvenience.."
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.