Yes, specific moves change, principles don't. I had to learn some new techniques when I started Judo, but did I have to learn how to fight again? No, and there's no crossover in those rulesets at all. I'd bet if you were asked to do a wrestling or a judo match, you'd do better than you'd expect just because you have an understanding of fighting developed from tkd and hkd. That's usually my experience.
EDIT: I guess it has a bit to do with your learning style as well. I am not one to learn things step by step, I'm a big picture person. Probably why I see things this way. For example, now that I have an understanding of what I'm doing when I spar I don't even really pay attention to my stances, or my hand position, or anything else.