Whiteboard interviews might miss eccentrics who can't express their clever thoughts verbally or visually, but it can depend on how tuned in the interviewer is to these eccentricities or how much value their team puts on expressive skills.
Algorithm/data structure interviews, whiteboard or not, also have the added benefit of being exceptionally good at eliminating candidates that:
1) Drastically misrepresent their skills
2) Give up easily at difficult tasks
3) Don't seek help from others
4) Frequently have a bad attitude
I had them attempt to solve the problems on a whiteboard that I would give to our intern candidates. Both totally bombed hard, and our other "re-interviewers" had the same result when they asked some design-related and algorithmic related questions.
This wasn't "regurgitating algorithms". It was basic problem-solving and software design. From their track record of development we didn't believe them to be qualified (despite their own opinion of themselves), and they only confirmed it by totally bombing the "re-interview" process (which was identical to our normal interview process).
The only way to validate your highering process is to randomly accept people you would otherwise fail. Anything else is meaningless.