Yes, I agree that SQLite is not suitable for multi-user Client/Server applications because of locking issues, but it is fine for a simple web site where you have essentially one client (The web application.).
A relatively small numbers of concurrent users can be served with the EXCLUSIVE, SHARED and PENDING locks in SQLite Version 3+, but the authors caution against use of network file systems. You can however write applications that rely on you being able flush data to a single disk by a remote client accessing a particular server process, this allows multiple applications to access the same database at the same time.
However, as you say, for a traditional Client/Server system you need to use a Server Database. There is a beta version of server type product SQLiteDBMS (sqlitedbms.sourceforge.net), but not much seems to have happened with it for a year or so. Or there is a commercial product that is very similar to SQLite from realsoftware.com, but that costs real money and seems to be for 10-50+ concurrent users. Postgres works for me, as most triggers etc. export fairly easily from SQLite...