Problems on a whiteboard don't test programming skills simply because the whiteboard isn't executable. You don't get the feedback that REPL gives you, so you can't build up your solution - and understanding of the problem - iteratively.
Strange argument. What are people who write in compiled languages supposed to do? Particularly if their code is part of a product with a long build cycle?
It's not like nobody has enough computers so you have to use whiteboards.
On this I agree. We switched from whiteboards to giving the candidate a laptop, their editor of choice, and access to a compiler and the manpages and this was a major improvement.