I agree that it is a glaring assumption, and perhaps is "culturally" biased. Someone programming in Perl or Python, would probably be very familiar with the built in data structures (hashmaps, dictionaries) but may not be familiar with others.

And this is exactly why I would give the programmer the benefit of the doubt. If they are able to implement a binary tree then I wouldn't hold it against them (and I hope most other programmers would extend the same courtesy).

However I have never met a programmer who did not know what a binary tree was.