In this case, JJ was wrong, you did need to know Trek to fully "appreciate" the inclusion.
I'm being approached by friends who know I'm a diehard fan, and they want to tell me their thoughts on STiD. They've only seen ST (2009) and now STiD, had scant knowledge of who Khan was, but still loved the new movie! Had they been confused, I'd agree with your assertion. But they had no questions about Khan or his motivations.