HighWind
As a European PPL we have learned the priority between different types of R/T communication, where ‘Mayday’ have the highest priority, and ‘Pan Pan’ have the second highest priority.
A European PPL could in principle be flying in US airspace without knowing that he is expected to back off when the world ‘Emergency’ is used.
It is important that we all use the same standard ICAO Phraseology, whatever that is.
As a pilot, it's your responsibility to familiarize yourself with the rules and regulations of any country you operate into, whether it's FAA vs. JAR-ops or differences country-to-country to ICAO "standard". In this case, the FAA's "Emergency" supplements ICAO phraseology as long as it's used in the U.S., it doesn't negate it. But this recognition of ICAO phraseology doesn't negate your responsibility to know FAA phraseology as it relates to regulation while you are operating in the U.S., or to comply with it.
It's no different than my responsibity to know what the Transition Level is in Qatar, the max holding speed at 6000' is in Germany, the Chinese metric altimetry system, or Brit ATC legalese when they aren't coming up with a new way to phrase clearance to climb on a SID and what they mean this month. When I operate in those countries, or anywhere else some of the other hundreds of differences that exist, I'm expected to know them.
I've converted my ATPL to 3 additional licenses over the years expat flying and taken a respective Air Law test for each one, and not one of those was mere transposition of ICAO-standard rules and regs. Perusing the "Differences to ICAO" section in the Jepps is routine part of flight planning into any country; there's plenty there to read. You're kidding yourself if you think you can close your eyes, point the nose across all borders, and depend on "ICAO-standard" to see you through.