And should this system fail, or simply be faked, how would I know?
PublicVotes' first claim is to be "fair". Fairness is a property of the form of election (eg approval voting vs first-past-the-post), not the voting system. I'll scan the docs, see if there's any merit, but right out of the gate the starting assumptions are way off base, so don't have much hope for the rest.
Instead of casting your vote by giving it to a single person you give it to many different groups interested in keeping the election fair. These groups can be anyone -- advocacy groups, political parties, independent auditors, or local governments. They all receive your vote, verify that it's correct, and sign their name below your vote on a public ledger which can't be tampered with without everyone knowing.
Hell, you don't even really need a digital blockchain for this kind of system to work.