It is a coping mechanism, much as guys in military combat MOS's have a similar dark sense of humor. 

Sadly, it is widely misunderstood by the public, so for those working long-term in EMS/fire/LEO, you learn the hard way to always "check the room" before they start with the "first responder humor" to make sure there are no non-first responders in the room - because that humor could end up causing PR problems for the agency or management in a short time. This is especially true in the era of ubiquitous cell phone cameras, social media, etc. 

Some EMS agencies I know of have strict "no personal cell phones on the job, period." Others have a "no postings made from the job to social media, ever." I know of one flight paramedic who took a picture of a sunset over the Colorado Rockies from the PC-12 aircraft she was in, and she posted it to the Book of Faces, and when she landed, she was fired on the spot. The company management said "We said 'no postings made from the job to social media' - we meant it." Mind you, flight medics are not a dime a dozen, so it inconvenienced the company plenty to fire her, but the consequences of social media postings of dark humor and scene photos have cost companies even more, so they needed to make sure that employees knew that management meant what they said.

What I've also noticed is that there are waves of people (often young women) who think that EMS would be a cool job ("because I'd be saving lives!" they happily proclaim) but after somewhere between a month to two years on the job, they're complete wrecks off the job because they cannot compartmentalize what they see and how much they allow it to affect them.  The shortest I've seen a person last in a EMS job was about four months, and this young woman could not handle the "first responder humor" when there were no members of the public present. 

The most annoying question I've been asked repeatedly by the public is along the lines of "what is the worst thing you've seen?" This makes me want to really go off on some people, because "what if the worst case situation I've seen were your relative?"  Do these people want me describing their relative's death to strangers? Do they think I relish the idea of revisiting some of the crap I've seen? No. Sadly, aggravated assault is considered a crime by the legal system, so you cannot really fix the problem.