The med crew where I work call the helicopter  

 as they leave you alone to do your thing let them call it anything they want to.  You will never win an argument with a quasi-customer who allege to be team members.  If medical characters are aviation team members they wouldn't constantly be trying to stick it (you're free to figure what) to their counterparts and the pilots and mechanics.  Comes with the territory.  Why?  Haven't a clue, don't care, and doubt anyone will ever put their finger on the answer to that one simply because it has been going on from the start of HEMS/HAA.