I'd be interested to read more about how much of the Special Forces difference they're born with and how much you can train.
A lot their "training" seem designed to weed out those who lack specific innate traits. From what I understand the goal is to cull most people as soon as possible and then train those who remain which suggests they focus on innate talents rather than testing people after they have been trained. Which IMO is a good idea, because you don't know what you are going to face in the real world.
PS: You see the same idea with a large high school's football camp. The first few days is all about weeding people out based on physical fitness.
I don't think it's entirely about innate traits. There's a lot of training that occurs before going to some these schools. For example, in the Army you're not eligible to 'try out' for Special Forces until you're an E4 grade (not sure about officers), which may take 1.5 - 3 years to achieve, assuming you enlisted as an E1. Even then a lot of guys spend 2-4 months in special training programs before going and some don't pass until their second or third attempt.
basic...AIST (infantry)...airborne...SFAS (special forces selection)
Personally, I feel I'm better able to handle stress after a significant amount of Brazilian Jiu-Jitsu and MMA training. This makes me suspect personal experiences make a big difference.
There isn't much to Army "training". Learn the specifics of weapons and kit, and then point and shoot, really. What separates a good soldier from a mediocre soldier is willpower. Good soldiers make the correct decisions more often because they can think clearly over pain, discomfort and stress - exactly what the article says.
SF training put a hyper-focus on this skill. So, to answer you question - pretty much all of it is innate. That has certainly been my experience. Some people are just better at this stuff than others, just like some people are better hockey players than others, even after years of training.
Maybe some of these calming traits can be achieved through medication?