I learned the common search algorithms in school. I haven't had to touch them since, if you asked me to write psuedo-code for them on the spot I'd almost definitely fail to implement them properly. There's a huge difference between struggling to understand something and not being able to do it from memory on a whiteboard.
Imo conversational questions are much better indicators in an interview of whether someone will be a good hire, the candidate knowing why you would use a binary tree over another data structure offers much more insight than asking them to write one. The more conversational approach also allows the interviewee to demonstrate their knowledge and gives you a better idea of how they approach a problem or whether they'd be a good fit on your team.
As a teacher I'd say that depends. If it's relevant to the job, then you should obviously know it, and perhaps even be able to expand upon it. Though after reading the posts here I have a sneaking feeling that things like that usually aren't relevant.
With that said, having a conversation with someone solving a problem right in front of you, gives you a very good insight into how the person thinks. To that end I've censored a lot of pupils where they have to "defend" (i.e. talk about or explain) a piece of code that they made, sometimes beforehand as a bigger project, or sometimes on the fly.
I'd often give them extra problems and talk with them about it as they solved it if I was unsure about the grade. I find that this gives me far more insight in where the pupil is coming from, and hence his level of competence, rather than seeing the code on its own, or having him answer a multiple choice or SAT type test. I can see how an interviewer might make use of a similar technique if he's unsure about the candidate.
Imo conversational questions are much better indicators in an interview of whether someone will be a good hire, the candidate knowing why you would use a binary tree over another data structure offers much more insight than asking them to write one. The more conversational approach also allows the interviewee to demonstrate their knowledge and gives you a better idea of how they approach a problem or whether they'd be a good fit on your team.