Mr. Woodham is simply saying that the presence of a negation in the if-clause does not change the basic idea behind the third conditional, namely, that it contains counterfactual statements -- statements that are the "opposite" of what actually happened.
If I had seen the approaching car, I would not have crashed into it. [I did not see the approaching car. I crashed into it.]
If I had not seen the approaching car, I would have crashed into it. [I saw the approaching car. I did not crash into it.]
In Mr. Woodham's way of explaining it, the first sentence talks about something that didn't happen (seeing the approaching car), and the second sentence talks about something that did happen (seeing the approaching car).
You can combine both ideas into one by saying that the third conditional talks about things in an "opposite" way -- counterfactually.
CJ