Maybe a better way to put it is, the whiteboard problem itself is a pass or fail question and therefore that aspect of the interview by itself is unbiased.
At google some candidates who failed all their interviews were hired because they had connections to upper management.
Here at Amazon, if the candidate knows the hiring manager and interviewers they can be fed all the answers. Not being able to code fizzbuzz doesn't block people from getting 350K+ offers. It's insane. Amazon tried to fix this problem with "bar raisers" but it doesn't work since humans naturally follow the crowd, even if the crowd is corrupt.