I am going to take the risk of looking like a complete idiot, here we go.
At first, I thought he was wrong. Then I realized, he might be right, but not for the reason that he explained. I think that in his diagram, one might argue that the fields have already travelled up the entire conductor length when he had hooked up the circuit. This also applies to any kind of capacitive or inductive effects. So, by the time he's closing the switch, the fields were only "waiting" to jump that final distance.
If there were two switches however, each placed immediately after the battery terminals, I think Derek would take the big L and have to wait his full second or more.