The article was specifically comparing database software, not entire systems; if your client is available when the DB is unavailable, then you can have an AP system regardless of the design of the database.
Exactly what I was trying to get at, thanks. The line between client state, server state and db state is a thin illusion. As REST makes explicit, every client operates on a representation of some server resources, which means CAP can come into play in even the most trivial online apps.