In this case it means that it could not write to 3 nodes, but it is not telling you if it did not write anything or at least once. Writing just once means that the data will be replicated.
So if only 1 of the 3 nodes is up, it will still write there and then return error, even if the coordinator knows that the other nodes are not up.
Queries have a maximum running time (only configurable at the database level if I remember correctly), and if your write exceeds this, it returns error. The replication still goes on and the data is still there.
Network errors are different category, since you might not even know if your command was sent or not. Cassandra kind of sidesteps the network errors though since the client connects to multiple coordinators in the cluster.