They seem to do this through instinct and play.
We all have instinct. It is there, waiting for us to make use of it. You only need to listen. And to develop the ability and skill to use it, play is a powerful ally. Hatsumi Sensei uses that word to describe our training. So is it part of your regimen?
From Neko no Myojutsu by Issai Chozan (1727):
... the cat replied, “Because of the self there is the foe; when there is no self there is no foe."When I was a boy, me and my buddies had many mock battles. Sometimes the whole neighborhood seemed mired in war. We took it seriously. But we knew it wasn't. There was a reality to our play that put us and our personalities on the line.
I see this in the dojo. Personalities are on the line. The training we do is serious, yet also play. How best to take advantage of that dichotomy?
More from Issai,
"Teaching is not difficult, listening is not difficult either, but what is truly difficult is to become conscious of what you have in yourself and be able to use it as your own. This self-realization is known as 'seeing into one's own being,' which is satori. Satori is an awakening from a dream. Awakening and self-realization and seeing into one's own being – these are synonymous.”
You must become transparent to Bushido, so that your training becomes a transparency through which light shines. This is the Budo in you, coming out through your training. Your instincts and natural ability will rise above the ego. Your eyes may open to see real Budo.
If you persevere in Ninjutsu as I have done, you will come to discern the ocean of difference that lies between things seen with true eyes, observed using the intuitive "feeling" you develop in this art, and those seen through the glass eyes of people who have not trained at all.
When he says "people who have not trained at all," I think that can apply to many people who visit the dojo and put on a gi. They go through the motions of training, but they are really not training at all.