Why does this need to be a public blockchain? Just make it a permissioned industry chain with access from each of its members. Someone lied, well they signed it

Why does this need to be a public blockchain? Just make it a permissioned industry chain with access from each of its members. Someone lied, well they signed it, go talk to them, you have immutable proof now. Or smart contract style, someone lied? Send the items back and escrow won't release your money as proof of return it could be signed by the courier and the original sender.