Of course, I can only speak for myself. I'm sure many programmers would immediately write them off.
That's a pretty glaring assumption, especially since it's subject to empirical verification. It also contains an assumption of its own -- that all programming needs a heavyweight familiarity with algorithms. There's a lot of programming contexts where the productive programmer just uses a hash so the mental bandwidth can be devoted to something else.
(FWIW, I do sometimes wish those programmers knew a little more about algorithms.)
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.