Chevron is not the only producer of petroleum products in the world and not every person in the world relies on Chevron's products every single day. It's absurd to call that statement factual.
As a simple matter of grammar, that's not what he's saying. He says that Chevron is a manufacturer of a "group of commodities" that "on which every one of us depends every single day." The sentence means that people rely on the group of commodities, of which Chevron is one producer.