This is something that bugs me about whiteboard-style interviews - they test almost none of the typical day-to-day aspects of programming. Without Google, without docs, without a REPL, without the code-run-debug cycle, how is it that you think you're assessing how effective I am in real life ? EDIT: not to mention that you're also not testing me for one of the most important abilities of a coder in a software shop: h…
When it comes to REPL and the code-run-debug cycle, they usually ask you to explain how to code would run to them step-by-step, which simulates having a computer run it. They do the same and pipe up if you miss something. So it's not the same as running the code, but it's similar enough and it also shows how well you understand the code you're writing.
I do think that the major flaw of whiteboard interviews is that it does not show a programmer's ability to organize large amounts of code. In most programming, you won't be solving logic puzzles as much as organizing several parts and sticking them together. The organization is far more important in the long run than the individual code itself, especially since the code will likely be changed later on (which is made easier if it is well organized).