She told me it's OK, he can survive with a B. What do you think? The entire point of the test is lost. He knew the material, and would have received a 103; instead he received zero. This was his first mistake in class. Is this extreme?
I imagine this teacher seeks to make an example of him, thereby reinforcing her strict rule about "pencil only" when taking her tests. That said, I couldn't accept any rationale for this educator's behavior. The intent of her tests is, as you state, to see if her students understand the material. You imply that your son's test score based on his number of correct answers was 100 percent or higher, indicating that he has a superior command of the test's subject matter.
Regardless of the teacher suggesting that he will still probably come out with an honors grade, he still should not receive this zero for this test grade. If you believe that you have gotten as far as you can using logic and reason with this teacher, I would suggest you take this issue to the principal of the school. I would hope that this principal would see the error in the teacher's judgment and focus instead on your son's obvious knowledge of the subject matter.