All the honest nodes are in a state of correctness, and will not commit any actions presented by dishonest nodes that attempt to subvert that correctness, because they will all arrive at the same result when presented with that data. Should some data from a dishonest node be accepted, then all honest nodes will retain the state of correctness, because they will all have committed the change from the bad actor.
The network split I was referring to was a not a malicious one, but a topological one. If one group of nodes becomes disconnected from the rest, they will form their own completely valid consensus within their own group, creating a fork. When they re-join the network, the fork will need resolving somehow?
This kind of forking will happen all the time due to network latency, the topological split is the extreme case.