I understand the skepticism, but there are reasons people would choose anonymity. If this hypothetical person wants to continue working in the White House, anonymity would be the only logical choice.When people post as anonymous, and/or use unnamed sources, I can't help but call bullshit.
I also think the NYT would be very aware of the tendency to doubt an unnamed source. That's why it is their general policy not to publish anonymous pieces. It would take something of this magnitude to warrant an exception.
Considering how our President accuses everything unfavorable of being "fake news" and considering how well it works with a large portion of his base, the NYT would have to be pretty certain of itself or be the most daring bluffer ever to roll w/ something it doesn't have a ton of confidence in.