Of course these types of people feel fear. Some more than others, some less. It depends on their training, and temperament, and the situation. Even in a combat unit it's highly likely at least one person is going to curl up into a ball and piss themselves while crying. Then there are the guys who run through a hail of bullets...

I think of it like Heraclitus; “Out of every one hundred men, ten shouldn't even be there, eighty are just targets, nine are the real fighters, and we are lucky to have them, for they make the battle. Ah, but the one, one is a warrior, and he will bring the others back.”

In the modern context, what equals out those numbers is largely training and muscle memory, so that once your adrenaline kicks in and your brain isn't fully functioning, you still know what needs to be done and can do it almost on autopilot. That can turn more of the 80 into the 9, so to speak, which is what a modern military needs.