Having gone through a handful of whiteboard-style interviews recently, I found that the opposite is true. If you can't remember the interface for hash tables in Java, for example, they usually let you make one up that you think makes sense. If you can't remember that "=" means assignment or that for loops need curly braces around them, you'll be in trouble, of course, but they'll help you with the details.

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).