‘Minimum Fuel’ Doesn’t Mean Priority ATC
According to the Aviation Safety Reporting System (ASRS), pilots might expect to receive priority handling after telling ATC they have “minimum fuel,” but

According to the Aviation Safety Reporting System (ASRS), pilots might expect to receive priority handling after telling ATC they have “minimum fuel,” but ATC is actually under no obligation to provide priority handling unless the pilot declares a “fuel emergency.” A recent ASRS report underscored the issue dramatically. An MD-80 captain, apparently expecting priority handling, advised “minimum fuel” three times–the last time when he was told he was 15th in line for landing. ATC declared an emergency, assuming the crew was reluctant to use the “E” word. According to the pilot’s ASRS report, “We landed with approximately four minutes of fuel before we were
in an emergency fuel status.”