In over 25 years of interviewing candidates, this approach has never failed me. I've never asked for whiteboard coding. Whiteboarding architectural concepts, sure.
The only caveat is the interviewer needs to have substantial experience in the same field to spot the wheat from the chaff in a casual conversation. If the interviewer is very junior, I can see how this might not work. Solution: don't have your most junior people run the interviews.
I agree asking highly specialized, deep CS-algorithm type problems is usually a terrible indicator. I typically start with a very rudimentary question that could go off in various directions and to various depths as time/progress allows. I let candidates choose the programming language, and to use either whiteboard, pen & paper, or laptop with choice of IDE.
I've seen candidates who claim to have years of "senior" experience struggle to get the basic syntax of their "language of choice" right - to the point where a competent hobbyist who spent a weekend doing a couple tutorials would wipe the floor with them.
There's just something about coding that makes it impossible to truly evaluate a candidate (for a developer role) unless you see them actually code.
It makes zero sense that someone can have a deep technical discussion but they're not able to write fizz buzz (which by the way is a crap exercise). Sure, if one is asking general questions about agile, TDD, SOLID and other fluff, anyone can answer those.
I have no way to prove to veracity of my story, so feel free to add it to the "urban myth" pile. But it was extremely bizarre to experience.