My perception is that the prototypical observant believing first responder can be convinced that there comes a point where God's will takes over, despite his/her ministrations. When the believer assumes that, following the death of the body, the next moment the victim will experience is eternity in paradise (hopefully), then the loss here on this planet becomes a gain for heaven.

Meanwhile, the atheist first responder may sincerely lean toward secular humanism. This first responder recognizes that the life he/she is protecting, or attempting to save, is the only life that the individual in harm's way has to live. Thus the atheist is open to a greater sense of loss, whenever a patient or victim dies.

When I awakened from the stupor of my religious upbringing, and recognized the uniqueness and temporal singularity of each of our lives, the value I placed on human beings increased exponentially.

I was a firefighter some years back and this sort of thing never crossed my mind. A few house fires, one with a fatality. Plenty of accidents with a few requiring calls for flight for life. Took 4 hours for one time for an accident to free the person who was in and out of consciousness screaming every time he would wake. You were trained to do a job and save people. I am sure there were religious firefighters who would say prayers but if you weren't you just did what needed to be done knowing that was what you were trained to do, try and save the person.

There is an Military group on this site...Foxhole Atheists [agnostic.com]

I think that you will find that all branches of the military have a diverse population ---Wiccans, Buddhists, Orthodox Jews, Atheists....etc.
You can also put anything you want on your dog tags...e.g. Jedi, Pastafarian, Cult of Cthulhu

[militaryatheists.org]

[religionnews.com]

[militaryatheists.org]

Whoever told you that is relying on the same old mantra of fear. I’ve been an open heart/ Cath Lab nurse for 25 years, moon lighted in the ER. I left the church when I was young, I separate my beliefs from my patients. I’m an expert in my field because of years of education and training not because of a mythical deity. I take comfort in knowing that when I die I return back to the earth from which I came. I’ve seen many people die unfortunately, there’s no mysterious glow or ghost or spooky shit. People just can’t let go, that’s why they believe in the afterlife.