By that definition, proof-of-work is also not objective, because you don't know which hidden chains are the longest chain. You are trusting that the sources who send you chains are omniscient.
That's a fair point if you look at objectivity in a strict sense. However, practically, it does make a difference if you only need one honest and omniscient (or at least up-to-date w.r.t. the longest block chain) node to get the latest state of the network. If you can connect to an unbounded number of nodes, you can asymptotically achieve objectivity since the probability that one of them will send you the longest chain will approximate 1 provided that at least one out of all nodes is honest and up-to-date.
Whereas with subjectivity, different nodes might come to different conclusions if some of the nodes are malicious.
Vitalik's entire premise was undecidable and irrelevant.
Vitaliks definition is too narrow and thus irrelevant.
Even if we are talking about "asymptotic" objectivity, its impact on security (and partition tolerance) of a decentralized network seems questionable to me. You cannot download and use the network client without trusting anyone (expect if you are the creator of the network) because you can never be sure if it's the right client or just a malicious copycat that is perhaps using a different protocol.