The crew never declared emergency , they just requested priority for approach because of a fuel problem. ( sollicitamos prioridad para la approximacion...problemas de combustible"
A huge difference for a controller and especially if you are dealing with a diversion with a similar request at the same time ( the Viva Columbia)
Declaring emergency as soon as the reserve was gone would have probably saved their day , got a direct much earlier and eliminate holding.
Avianca 52 all over again ...(for those old enough to remember, for the others, go to Google )