Actually, that Avianca crash in New York was an example of something other than a steep authority gradient, if I remember the report correctly.
From Wikipedia:
The report references the 360° turn that the flight was ordered to make at 20:54 as evidence that the crew should have known that they were being treated routinely and not given any emergency priority. Instead, the CVR revealed that the flight crew was convinced that they were being given priority. Additionally, the NTSB criticized the first officer for failing to use the word "emergency" as the captain had insisted he do. Compounded with the apparent inability of the captain to hear or understand the radio communications, the NTSB called the situation a "total breakdown in communications by the flightcrew." Summarizing, the investigators cited "the flightcrew's failure to notify ATC of their fuel situation while holding at CAMRN in order to ensure arrival at the approach fix with an adequate approach minimum fuel level and a breakdown in communications between the flightcrew and ATC, and among the flight crewmembers" as the two main factors that led to the crash.
For some unknown reason the FO did not make a "Mayday" call as he had been ordered to by the Captain, so that this accident was not due to a steep authority gradient but something more the opposite.