The word EMERGENCY would've made a huge difference if the crew used it.
And you're right, ATC did not know who to prioritize that night that's why the 707 fell out of the sky. Maybe a few more aircraft were reporting low on fuel that night as well. So, I guess it all comes back to their training and company procedures on deciding who to prioritise and if the word "emergency" was still necessary for them to hear or at least confirm.
In comparison, Sydney Radar did ask me if I was declaring an emergency when I requested a 180 back to BK when I told them my right door have come loose and partly open ( maybe it was part of their training to ascertain ). Maybe JFK should've tried the same thing, and include it in their training.
Onya Syd Radar
D6