How is a binary search not mimicry? Probably only 1 in a million people could figure out how to do it if they didn't already know how it is done elsewhere. The only reason most people know how binary search works is because they were taught it somewhere along the line.
Ask an interviewee how to Voronoi diagram the surface of a sphere or something. Then you'll see how things look when people don't do mimicry. You don't get original ideas by asking first-semester programming puzzles.
It's a pretty darn obvious thing to do when you're physically handling an ordered collection of records.
But I agree, plain vanilla binary search is easy.
But all that's irrelevant to my point. Asking for a bog-standard solution to an industry-standard question is in no way a demonstration of someone's originality. You don't ask it to prove that they aren't doing "mimicry" you ask it to prove that they can, and thus are capable of learning the basic tools of their trade from others.
They already know how it is done elsewhere; it's how one finds a word in a (paper) dictionary or an book index.