Asking the right questions at interviews are crucial for finding the right people. If a candidate for a programming job knows binary trees but doesn't listen to other peoples views I would say he's less worth to us than a listener that easily learns new concepts but is currently not familiar with binary trees.
BTW, leaving a candidate in tears is not professional recruiting. Please let someone with more people skills accompany you to your interviews, you might leave people with scars that takes years to heal.
I'm sure it's used under the hood in a lot of code I write and have written but so is XOR, manual memory management and a bunch of other lower level implementations that I don't need to spend time on when developing on a higher abstraction level.
Not sure why you would expect all programmers to know about binary trees specifically.
I'll bet, even with this feedback, you'll continue to ask that question, just because.