Was the a/c operating under a PAN? The use of 'emergency landing' is used for any event where it lands not at planned destination or alternate. Once 'emergency' is released on the airwaves all services sitting bored seem to want 'to be seen to be doing something'.
I remember an event many years ago where a UK a/c shutdown an engine, perhaps even a fire, and diverted to LPL under Mayday. That kicked into action all sorts of unknowns including alerting all hospitals within a radius and calling extra fire brigade from down town. In the subsequent haste to reach the airport the fire engine crashed into an innocent car and the driver as killed. The a/c landed safely and everyone else survived.
I've had various differing advices from airlines about when to use PAN or Mayday. Each seemed to have their own opinions. What we were not told is how ATC & Airfield procedures reacted to each. IMHO that is very relevant information for a captain. I know there were some old dogs who always wanted a Mayday to clear the skies for them. "Who's ever heard of a PAN outside of the classroom". Grump. Others were Mayday first then downgrade; others were wait and see what the condition is after you've actioned the QRH.
In all their advices there was nothing about what the rest of 'the team' were doing in the dark.