The Times DID publish a generic privacy policy article a week ago and it did call itself out as one of the worst ones [1].
It wasn't an explicit "at the Times we do this", but there's an infographic/chart in the article that places the NYT in a pretty damning spot[2]. They also called out a rival news organization (the BBC) which does a great job relatively speaking.
I think the Times has a huge point here in general and I find this article's narrative compelling and well done. Instead of making it about "why didn't we make this about themselves" I would rather focus on what it's trying to say. (Also, Google is probably the trailblazer here with this stuff and sets the tone/trend).
[1] https://www.nytimes.com/interactive/2019/06/12/opinion/faceb...