How is this being solved by a block-chain?

You still need to trust all the people in the production line (Farmer, Juicer, Seller and not to mention that transportation guys) that brought the bottle of juice to market to actually record things correctly into the used block-chain.

The trust required in the data entry "Link/Step" basically results in the use of a block-chain to be pointless, as trust is already a requirement in this particular chain of custody.

This is also why the block-chain only really works in Digital Only assets, as you link the asset it self in the block-chain itself.