He doesnt actually justify the claim in the title anywhere in the video, he just states it. It's not insensible but I think either he did not adequately explain it or the video was cut short.
Interesting video on money, quite a different take than I hear from bitcoiners: https://www.youtube.com/watch?v=X-D5FERQzU4
My summary of the video: There were never any barter economies. Money predates writing (the oldest writing cuniform on clay tablets were accounting records). Money is always tightly tied up with state power, primarily because states can enforce payment for debts owned which originated from people accidently harming other people.. the governmental power steps in and says "A owes B X amount of state-approved money to make this right." Thus, the value of a currency without intrinsic value is imparted to it by the power of the state that controls that money. Taxes just tie it even tighter to the governmental power. Every central power (state) has it's own money, with few exceptions (e.g. the Euro experiment, which is failing).
Discussion
So I went and watched the entire video this is cut from here https://www.youtube.com/watch?v=E5JTn7GS4oA
He states later that the claim in the title is a story they tell to get you to focus on money as debt, just as the story of medium of exchange being a commodity to eliminate coincidence of wants is a story. It doesnt matter if it's true being his point, the story is to convince you of the theory by directing your attention so that you view money a certain way.