I have yet to encounter a situation in my career that called for a binary tree. I use general trees and graphs all the time, but never any of the specialized forms.
Maybe the problems your companies have worked on did. That's fine. Don't go telling people to "stop asking people to pay you to write software" just because they don't know how to use or write a binary tree, though.
I agree with you that I wouldn't hire someone who doesn't understand linked lists, but I still think your statement is too harsh for that situation as well.