It seems this criticism is of the interviewer making a poor decision based on missed/incorrect observations, not with the whiteboard interview itself.

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