I realize that a student will occasionally get a particular question right by a method that she cannot write down, and also that, even more rarely, whatever way she got to that answer is actually a sound method rather than luck, but I question whether it is frequent enough to invalidate the advice you quote. In my experience, most of the time when someone does not know how to solve a problem, he cannot solve it in his head.

As you say in your last paragraph, "If they're not writing down the steps, it's more often that they are demonstrating that they don't have a good enough level of understanding to do this", but that is not the situation addressed by the advice you object to. If they are answering the questions in their heads without understanding how to solve them, the questions would not seem to be a good match to the topic. If they do understand how to solve the problem but don't know how to put it in words, again that is a different problem, possibly in how it has been explained to them.