Declaring an emergency
In US "I'm declaring an emergency" then stating the nature of it, is PERFECTLY acceptable. Roll the trucks as previously noted is everywhere in US understood by controllers. Flight checks and real emergencies have some things in common, but in the situation here, stress can get the better even of fully competent professionals. Admittedly, in other parts of the world, roll the trucks may not be understood. In my opinion pilots did a GREAT job. Controller should respond to the transmission first and ask questions later.