You wouldn't trust the Chinese supplier (or any supplier). You'd go to the bauxite shipment company and let them register with the network, you'd send independent auditors to their premises, very much as we do it with ibdependent audits nowadays.
We do need to physically access the premises across the supply chain to verify that 'on-chain personas' reflect their 'real' identities. But no single authority can control the data, we can be quite sure that all transfers of ownership across the supply chain have been authorized by their controllers. Compared to centralized systems, the blockchain provides us a much higher level of transparency and certainty over the fidelity of the information.