[KhanMahGretsch]

Thanks for elaborating so well on your initial premise, I think you bring up some good points about how this kind of interactive problem-solving can be an effective tool available to the interviewer. For better and/or worse, there's a reason why it's so prevalent now and controversial.

I'm inclined to describe it as a sort of interrogation technique, you're offering a stimulus (the problem) and aggregating a number of reactions to form an opinion, and open up new lines of questioning. Very delicate work.

I think problems arise when unskilled interviewers present an excessively obtuse problem to the candidate, then read far too much into their responses (this approach is also easily "hacked" by those who've memorised common problems of this ilk). To stick with my interrogation analogy, it's the equivalent of screaming in the suspect's face, noticing that they gulp before shifting in their seat and scratching their face, then deciding that "they must be lying".