Mayday fuel is a thing. It is in the ICAO standards and the EASA regulations. As most countries do not speak English as their first language, how words are phrased remains important. Using the word "emergency fuel" for instance in some countries may not register an urgency because their controllers are specifically trained to give priority handling to an aircraft declaring Mayday fuel. After all, that is what is in their regulations.
Even though the FAA regulations do not consider going into final reserve fuel as a distress, that does not mean the pilot does not have the authority to declare a Mayday if such a situation were to arise. The pilot always has that right. Going into the last 30 minutes of fuel is not a fun situation to be in. Especially in a jetliner flying at low altitude.