Okinawan karate seems to use an apprentice model of conveying information to its students. Technical proficiency is hammered into the student over several years with very little overt reference to the applications found in kata.
In many respects it is up to the student to determine what the applications of the kata may mean under many, many years of guidance. I know I have rambled about this previously, but its worth repeating; Kanzaki Shigekazu (a student of Kyoda Juhatsu) has continually stated to me that Kyoda never overtly taught kata application and only ever alluded to it.
In a conversation with Joe Swift he related that the same teaching model was used in a discussion he had with Kinjo Hiroshi (student of Oshiro Chojo and Hanashiro Chomo). Kinjo sensei, like Kanzaki sensei, stated that the emphasis was on executing proper technique; not teaching what the kata meant. For the most part it was up to the student to figure things out with hints being dropped by the teacher from time to time.
I think techniques of kata were generic in some respects. They contained movements which could be used in a variety of situations. I like to use the explanation given by Wade Chroninger, that kata does not teach specific movement per se, but instead it teaches implied movement. That is, movement which can be used across different situations. If kata movements were intended to counter only one specific technique, then it would be necessary to memorize and practice literally hundreds of kata. This is why I feel that the current idea that kata as a solo reenactment of a two-person set may not be appropriate. The Okinawans, as we know, were much more pragmatic than that and were more interested in developing spontaneity of technique IMHO.