This is how news reporting works. The sources are not willing to speak publicly because they're talking about classified information. The NYT has verified their identity. You have to trust that NYT is right.
I realize that's an unsatisfactory answer for many. But it's how journalism has to work sometimes.
You said:
> We have on the record sources
You are not on the record if you are anonymous.
Yes, you are. On the record just means “for publication”, as in, you are aware that what you’re saying is going to be repeated publicly. The phrase has nothing to do with public attribution.
> On-the-record, in journalism, means anything in a communication may be publicly disclosed
https://en.wikipedia.org/wiki/On_the_Record
Funny you link there and not the main article that contradicts it:
> "On the record": all that is said can be quoted and attributed.
> "Unattributable": what is said can be reported but not attributed.
https://en.wikipedia.org/wiki/Source_(journalism)#Speaking_t...