Can a blockchain offer transparency to a humanitarian aid supply chain?
It would largely function by pictures I would imagine. Let's say, for example, each crate of goods had a QR code, EDIT: with the private key known only to the supplier. 

So the supplier gets these QR codes(public keys) , slaps them on the crates and sends the crates on thier way. The receiving end then must provide not only a video of those crates being opened in a food distribution center, but the video must include the QR codes in the footage. Then the supplier will know thier goods have not been hijacked, particularly if the video includes the goods being handed out on camera.

Those videos can then be published along with the QR codes for external verification on a blockchain.