That is kind of it, sort of. Koans are aimed at our conditioning. People can spend years trying to solve them because koans have no rational answer. On the other hand some of these stories relate the moment a person woke up, but do not reveal what went before, things like years of meditation or trying to solve these riddles, beforethe person was ripe to wake up; the nature of reality is buried in these stories but it may never be immediately evident. The experience is so difficult to relate because it reveals something that has always been in full view so to speak.
For example Bankei Totaku, a 17th century Zen master had his first awakening under the following circumstances: He built a small hut in the nearby village of Nonaka and lived as an isolated hermit. He sat for long, rigorous hours immersed in zazen meditation. He abandoned all bodily comforts and focussed intently on arriving at a complete understanding of life and phenomena. 'Often I would go into the mountains and sit in Zen without taking a morsel for a week, or I would go to a rocky place and, choosing the sharpest rock, meditate for days on end, taking no food, until I toppled over. The results? Exhaustion, a shrunken stomach, and an increased desire to go on. I returned to my village and entered a hermitage, where sleeping in an upright position and living arduously, I gave myself up to the old spiritual exercise of repeating the name of Amitābha. The results? More exhaustion, and huge painful sores on my bottom.' Eventually the complete neglect of his body led to serious illness, tuberculosis. 'Soon I was bringing up blood, lumps the size of the end of my thumb.' He sought a doctor’s care, but the physician issued a prognosis of death. During this near-death period Bankei attained initial enlightenment or kenshō. He later described the epiphany: 'I felt a strange sensation in my throat. I spat against a wall. A mass of black phlegm large as a soapberry rolled down the side; suddenly, just at that moment, I realized what it was that had escaped me until now: All things are perfectly resolved in the unborn 'It struck me like a thunderbolt that I had never been born, and that my birthlessness could settle any and every matter.' After this, his health improved, his realisation deepened and he went on to teach. But that shows you the odd circumstances under which awakening might occur, in this case it was looking at a glob of his lung sliding down the wall. It is not necessary to get ill like this, but it takes a certain kind of resolve to follow through because you may never have any inkling of when it will happen, that what is blocking your experience of seeing through the riddle of life will, lift off. You might be looking at potatoes in the market, sipping coffee, or hearing a bird in the forest. At some moment the block gives way and the dam breaks open; you can't predict it, and it's not that the situation is the trigger, it is just time; maybe the situation is simply a coincidence, but of course you remember what you were doing when it happened. The mind remembers striking events more readily than mundane ones. On the other hand some may just gracefully slide into the experience. I suspect this happens gracefully more with TM meditators, but that is just a suspicion. Because the experience is not what people expect (because it transcends whatever you knew up to that point), it might even be doubted, and you might think you have lost your mind. I think this latter might be what happens if the person had very strong beliefs that enlightenment was going to be some specific particular way beforehand, and then when it does not turn out that way, the mind has trouble resolving the experience. And for most, resolution of the experience, the way it settles in, the way the implications take over one's life, takes some time, usually years, regardless of whether one understood clearly what happened or was nonplussed by the experience.
