I think maybe its time for USA to follow ICAO rules and recommendations...
Then the pilot would (should) have used the terms MAYDAY in the emergency call...
The pilot should have had enough fuel to make it to its alternate aerodrome plus a missed approach at alternate (what are the FAA requirements?)
From an ICAO perspective, the pilots decided to continue without following ATC instructions (which is all good and well if he was in dire need and the plane was in critical danger if he followed ATC instructions - but this doesnt seem the case?), so how low on fuel was he?
I think the biggest concern is not pilot vs ATC, but FAA vs ICAO.