Blockchain guarantees unforgeable results. It isn't about privacy or anything. After some information gets appended it is given an ID based on all previous information, so secretly modifying existing data or secretly inserting new data is impossible.

My guess about the US's use of it is that they only used it to ID real ballots. Ballots produced without the IDs would be identifiable as forged, the IDs could store their geographic area so ballots outside their appropriate area would be identifiable as stolen. Even if they managed to replicate the isotope watermark, if the IDs encoded are duplicate or wrong they'd be identifiable as forged.