The details provided in the response are probably being disclosed legally (doubt Amazon PR would screw up that badly), but it shows really poor taste that they would even respond to the NYT piece which was pretty clearly hyperbolic, emotional, and somewhat cherrypicked; even more so that they would adopt the same tactics of naming and shaming ex-employees.
The fact that it was also published on medium by the head of PR baffles me - why are they aiming this refutation at the tech crowd that would probably see through this cover-piece pretty easily, instead of getting it into a high-readership, Amazon consumer oriented publication? Poorly planned and executed all around, regardless of legality.