But... demonstrating the ability to write subtle code
is a useful question. "Describing" or "discussing" algorithms isn't the same thing at all.
I mean, I can't speak to the thinking of the original interviewer, but this is what I'm looking for with that sort of question. And I don't see how a binary tree is a bad choice. Again, it's something that everyone sees in school, so it doesn't require a ton of description in the interview.
I guess I put the question back to you: if you won't write a binary tree traversal in an interview, what subtle code would you be willing to demonstrate? And why is that better than a binary tree?