But imagine Einstein having to look up how to derive x^2. I'd say that's a pretty close equivalent to knowing tree traversal in CS. It should just come naturally.
I've been working in the programming industry for ten years and have never had to implement tree traversal. I could probably scrape together a naive implementation in a relatively short amount of time, but it's certainly not something I've memorized. But then, I'm a programmer, not a computer scientist.