This post is full of errors. For example, Paxos is not about the Byzantine General's problem, Paxos is a consensus algorithm for the non-Byzantine case.
The part that actually coordinates all the different network wrappers to work in unison is what makes a software "distributed".
The correct statement is "Paxos handles the failure of a minority of nodes" or "Paxos can make progress if a majority of nodes is alive and connected". Paxos does not deal with nodes that do not follow the protocol (ie. lie, have been hacked, etc, this is what 'byzantine' means). Paxos only deals with non-byzantine failure.
Thanks, let me know if there are other issues.