Deeply embedded meaning they have a deep network of sources, or deeply embedded meaning they are working in concert with American intelligence services?

The sort of quick rule I have for measuring credibility is "how much of a story is it when a reporter or outlet gets something meaningfully wrong?" For the NYT, it's a rather important story, like the Iraq WMDs you mentioned. Which, needless to say, was over 20 years ago.

We'll see what the truth ends up being with time.