They wouldn't allow you to substitute your own implementation? That's rather odd. I'd be more interested in whether you knew how to traverse a linked list than I would be in any knowledge of the Python API.
A white board interview shouldn't exclude naive implementations. After the naive implementation has been done it's reasonable to ask for less naive approaches.
Also the continual whining about white board interviews is tiresome. It's a fact of life that exists in almost any tech interview you do. Practice, get your friends to bust your balls before the fact, write itoa on a white board or detect a loop in a singly linked list and move on with your life.
At some point if you're going to get paid you need to demonstrate your ability, reality says the potential employer decides what type of proof is required.