As for "specific knowledge of wrongdoing"... well. What's "wrongdoing" here? Barr presented a summary of the Mueller Report to the public. Apparently, people in the investigation itself are unhappy with that summary and consider it deceptive (yeah, no shit, saying the Trump administration misleading people is like saying water is wet).
Yes, this is multi-layered, anonymous leakage, BUT. BUT. Is it untrue? Are investigators actually fine with the Barr summary, and the sources are lying to the journalists? Probably not. So despite the abstraction layers, the gist of the story is most likely true. And the NYT certainly doesn't have to run a story that says "Mueller is totally fine with the Barr summary" next week, so they're not going to print it unless they believe it true. So smell tests are fine here.
And the basic question is important. It's not whether Barr lied, but rather whether he intentionally misled - or more to the point, if Mueller's team believes he misled. That is relevant to the public, and to me.