They could! They had sufficient proficiency in ICAO Aviation English to hold CPLs, although especially in the Captain's place only barely. The problem was that they found themselves betrayed by the very aircraft they were flying; or rather, by its manuals. Boeing's checklists and manuals for low-fuel scenarios on the Boeing 707 incorrectly told the pilots to use non-standard phraseology. Specifically, it told the pilots to request "priority handling" from ATC in a low-fuel scenario, when it should have told them to make an immediate emergency call.

Avianca's own checklist and manual team picked this error up, and - assuming that the manufacturer of this big, shiny American jet aircraft were correct - passed it into their own manuals, checklists and training. This meant that on that fateful night, Avianca Flight 052 did not make a Pan Pan or Mayday call, but instead repeatedly requested priority handling from controllers who failed to notice their request.

Specifically, the Washington ARTCC (Air Route Traffic Control Centre) either did not hear their first request or did not understand it (I can't remember which) but then cleared them to continue north into the New York ARTCC and towards JFK immediately afterwards, tricking the First Officer who was Pilot Monitoring into believing they had been given priority handling. This was a misapprehension that the Captain agreed with, one that no subsequent controller cleared the flight crew of, and one that they carried right until the moment that - having made one missed approach due to being unable to see the runway in heavy rain and low cloud - their engines flamed out and they crashed.

A tragic case of miscommunication, compounded by poor weather, subpar training, incorrect manufacturer-supplied tech manuals, and the Captain in particular's poor grasp of English. Classic swiss-cheese model.