Michael - I agree with your post. Seems to me it was the PIC and the airline involved that chose convenience (possibly lots of paper work) over the actual emergency.
As far as declaring emergencies - "Brakes On" - stop the nonsense of US military denying aircraft entrance in case of an emergency - simply not factual. In an emergency any aircraft will be let in. Getting out might be a different, probably a pretty lengthy procedure.
Also and a little off the subject - I used to fly over the Cuban airspace heading to Cancun and the Cuban controllers were very helpful with weather advisories when asked. Their English skills were much better than in Mexico too btw. That's a different story.