The teacher has to offer what help is necessary at this level, but if he himself has spent little or no time in Asia, he can only offer so much. So even a student with relatively deep insight into the initial koan will have some culturally conditioned difficulties with later koans. And it's not just that such a notion would belie one's awakening. It's more than that. Other considerations include emotional maturity, how long the person has been practicing, and the soundness of his or her character.
Character is especially important.
As we know, if it is shaky, the insight can wreak havoc. Going by my contact with colleagues at our annual Zen teachers' meetings, and by my exposure to koan students at their centers, it's fair to say that in modern times passing one's first koan doesn't often imply an earth-shaking experience. Any way you look at it, it's just a beginning. Roshi once used the example of the sun rising. We begin practice at midnight, when it's pitch dark.