They probably understand the base meaning of the movements according to current doctrine, whether that be KKW or whatever TKD group you prefer to reference. I doubt most understand the context of the movements from an inheritance perspective seen through the lens of parent arts like karate or gong fu. I'll use the analogy of a palimpsest, where an old manuscript has been scraped of the prior writing and then is reused. Occasionally, some of the old text is still legible, yet it's impossible to obtain all of the old message since it has been discarded, changed, or written over entirely. This is what I refer to with regard to patterns. The patterns practiced in TKD undeniably have the stamp of other arts all over them, yet the actual sequence of movements have been changed and reshuffled. Thus, it's unlikely that anyone would have the same perspective as a practitioner of the parent art without intentionally seeking it out to learn it.
And yep, I have been in the martial arts a long time. Spent 10 years doing nothing but traveling the world to study various systems thanks to a trust fund. I've spent 2 semesters with exposure to a KKW 9th dan and his senior students both at college as well as at his dojang where my prior experience in other styles was respected. I've seen many expressions of TKD. Don't take it personally if my perspective is different than yours.