The P refers to partitions between nodes of the database system. Not clients.
So that point in the article doesn't seem to make sense.
You don't get nothing, you get inconsistency that could require even human intervention to fix. For example, if client lost connection right before the database was able to respond that his commit was successful. Client then retries and you get a typical double billing problem.
That's because monolithic database with a remote client is in fact a distributed system and strong consistency in a distributed system requires proper distributed algorithms and protocols, where clients are nodes too. You cannot guaranty consistency otherwise (to be precise, you will need clients to be able to wait indefinitely to guaranty strong total consistency, but if clients are used by humans they will not do that and the only consistency you can guaranty for a human is eventual consistency).
> But practically speaking these are rare; add remote clients to the monolithic Oracle server and you get a distributed system which can experience a network partition (e.g., the Oracle server becomes unavailable).