Ah, but call a trooper or a deputy a police officer or any variation thereof and they'll correct you... much the same way a medic will if you call them an EMT. Heck, call a Marine a soldier, and they'll correct you there too.
So troopers and deputies are no longer "law enforcement officers?" They're "law enforcement troopers" and "law enforcement deputies" now? Sure, there are some that are going to get uppity, just like there are the "ZOMG, I'm a PARAMEDIC not an EMT" or "ZOMG, I'm an EMT, not a PARAMEDIC" EMS providers out there, but I seriously have a hard time believing that the average high way patrol officer or sheriffs deputy cares what the average person calls them during limited interactions. There comes a time when arguing about titles becomes pretentious. What would you say if I insisted on being called a "student doctor" instead of a "medical student?" After all, "student doctor" is the proper title for what I'm currently am, even if I find it extremely pretentious.
It's not wrong to want people to call you by your proper title, even if the average person cannot distinguish you from someone else in your related field right off the bat.
It is wrong when you expect 100% accuracy in title in a field with multiple titles. I'd be more sympathetic if there was a single unified title, but there isn't and there's too much division and too much, "Mine, not yours, you can't have" in EMS in the USA for that to happen currently. I'm more sympathetic, for example, for providers in Canada where every provider in most provinces is a paramedic, be them a primary care paramedic, advanced care paramedic, or critical care paramedic. That's a harsh contrast to the US where you have EMT-1, EMT-2, EMT-3, Advanced EMT, EMT, EMT-B, paramedic, mobile intensive care paramedic, paramedic specialist, EMT-paramedic, licensed paramedic, EMT-Airway, and the list goes on, and on, and on.
Calling a medic an EMT or an EMT a medic is just a mistake of levels, not that big of a deal. Calling someone an ambulance driver is a mistake of existence. I don't call a cashier a "button pushing money taker" or a janitor (or floor technician) a "mop mover" etc etc. You don't label the person by a single task that they do in their job.
So fire department engineers need to be called something else then, because only a part of their job is being an engineer? Field training officers need a new name since field training is only one task? Additionally, when I'm describing a person doing a specific job as a part of a team, that job because a rather important title, especially when there's a vast difference in immediate priorities between the ambulance driver and the patient attendant, regardless of what their level of training and education is.