Breaking them down to find applications is not the same as reinterpreting what movements are in the form.
Thus the form is not reinterpreted, but a different application is found.
However, if somebody is reinterpreting the movements of the form to either be something other than what is in the form or to be executed in a way contrary to the way that the moves are taught in the system, be it Kukki taekwondo, Shotokan karate, or any other system that has a codified set of forms, then their understanding of the form is flawed.
In other words, if you do your Taegeuk pumse 'Shotokan style' because you feel that it has some benefit, then you are performing the form incorrectly and likely do not have the foundation to understand why.... and should probably be at a Shotokan school if that is what you are after.
That is a very good way to put it Daniel. Unlike the older TKD form sets which are somewhat reinterpreted Karate forms (i.e. high kicks vs. lower kicks, which totally change the intent of the movement), modern TKD forms are unified in standard because we know who the creators of the form are and what their intent of movement is, a.k.a. the KKW standard.
There are different 'flavors' of performing the older TKD forms, because, just as their Japanese and Okinawan counterparts, there is no one single unifying standard. This is not the case, as I understand it, with the KKW.
I have more freedom with intent, because I do practice the older forms, which as punisher pointed out, there are in fact layers of intent with the movements. I would like to point out, that when teaching these "layers," it does not change how the movement is executed, only a different intent with the movement.
Can you apply the same nature to a KKW form? I don't know since I don't practice them, but I'm confident that you probably could. The major difference being that, it sounds as though there was never multiple layers put in place by the creators of the form. So it is what it is. Like you put it, there is ONE, and only one, proper explanation to the movements in your forms. If you try to say that it IS a different movement, then you are wrong. IF, you practice other techniques that fit into the same movements found in your forms, then you may find some benefit for doing so, but that all depends on your focus of training.