If trusting Alice, Bob and Carlos's public keys is equivalent to trusting them, then I don't really need a blockchain to verify that they did what they said they did.
If it's not, then I don't trust the blockchain as a record of what happened, because there's no chain of trust between what they wrote in the blockchain and what they actually did.
The reason why this sort of thing works with cryptocurrency is because, with cryptocurrency, the blockchain is reality. If the blockchain says I have 1BTC, I have it. If it doesn't, I don't.
As soon as you try to apply it to something like supply chain management, though, that falls apart. The map is not the territory. So you have to add a whole bunch more stuff to the system to try and ensure that what's been recorded is accurate. Not entirely unlike how, in the story of the stone soup, people had to add a whole bunch more stuff besides the stone to the pot in order to make sure the soup was tasty and nutritious.