i don't think the top comment means literally a whiteboard. i think his argument is that if you can't program relatively basic things away from a computer, you don't really know how to program.
Someone standing behind you, looking over your shoulder, might be a bit intimidating at first, but if you have your reasoning figured out for yourself, there is no reason why you couldn't speak out your thoughts out loud and let others know the way how you came to a solution.
When you would ask me how I came to the answer, I wouldn't be able to tell you: I primed my brain and then eventually a lightbulb turned on.
But doesn't this just show that I'd never come up with a timely answer? Not at all. I took many tests as an MIT student in which I got A's and which I worked in precisely this manner. I didn't know how to solve a certain question, so I moved onto another question and then came back to the unsolved question. Often by the time I did, I just now knew the answer. On other problems, I'd do work and then cross it off and start over.
I could work this way because I didn't have someone staring over my goddamn shoulder asking me what I'm thinking every goddamn step of the way. If I have to explain myself constantly, I just get flustered when I realize that I said something completely stupid, and then I can't continue with my natural thought processes.
I cannot assert strongly enough, that the process that you claim that anyone smart should be good at, does not work for me.