I think whiteboard interviews are more about weeding out false positives than weeding out false negatives. While one might think they would be equally damaging, as in either case you are out one good programmer, the former (false positives i.e. hiring a lemon) is actually more damaging since you are in one negative. For why that might be, see one theory of production, the O-ring model [0].

[0] https://mru.org/courses/development-economics/o-ring-model