To be honest, I think there are somethings you have to be born with.
Not saying I am, or anyone I know is... just saying.
And yet, as others have pointed out, there are various kinds of training programs that are designed to teach people how to act in a crisis, without necessarily having had to deal with any real-world crises in the past. My EMT training was like this: deliberately stressful scenarios designed to simulate the stress of a real emergency (or, I suppose, to help people to realize if they're really not cut out for this sort of thing).
I think there is a difference, though, between this and the sort of "training for crisis" that one might do in aikido. While there are countless medical crises that can afflict the human body, they fall into definite categories, and there's a definite hierarchy of severity: faced with severe bleeding and a broken arm, it's a no-brainer which problem needs to be addressed first and how you need to address it. You can put someone through a training program that will teach the skills of assessment and tell them what the correct decisions are. I don't know that you can really do that with a sort of open-ended self-defense "crisis".