I took this from another question I had.
Under appropriate uses for sqlite it has:
Situations Where SQLite Works Well
•Websites
SQLi
"web" applications imply the browser is the client
Client/Server apps imply a custom client app. Think Outlook hooked up to exchange, while it may use the web to connect, it is its own client to the exchange server.
EDIT:
More specific to the sqlite text you posted, what they mean is that client applications shouldn't be accesing your sqllite DB directly, and instead should be using some sort of server side interface (i.e. a json web service)
But that rule of thumb, in my opinion, applies to ALL database engines. If I were using SQL Server or Oracle, I would DEFINIETLY avoid having client apps connect directly to the DB, this has many potential problems, the first being security.