The byzantine Trust issue is really just all agreeing on a a value. A handle/name and public key pair is such a value. We can distribute public keys in a block-chain. This pushes MIM attacks down to the last mile between a block-chain server and client and to the identifier exchange. The user can run their of own Block-chain server and authenticate via sneakernet if need be and we can at least be assured that you are communicating with the person who's handle matches the key (even if it might not be the person we think it is).

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A Blockchain makes a good backed for a web of trust because it lets us use the above to link an identifier with a public key and server. One of the primary scaling issues with a web of trust based authentication is that names get long fast: PersonA.PersonB.PersonC.Otherguy. A blockchain allows for a universal naming scheme and a central place to store high confidence links that is faster then querying the peers I trust and asking if they have a link to an arbitrary node.