That's not quite the same as you'd still need to have some way of exposing the database on a different machine. You could use NFS or some other network storage, but that's kinda hacky and doesn't deal with network failures well. (In fact, that documentation doesn't specify what happens if one database file becomes unavailable while you're attached to it at all.)
There are work arounds, of course, but I think it's a pretty big downside that it's difficult to set up robust replication with sqlite. It's certainly one of the things that cause people to say that it's not a "real" database.
You can also just (eg) copy the backing file wholesale. It's portable and endian-agnostic. I guess it depends on exactly what you're trying to do and what guarantees you're requiring.
There are work arounds, of course, but I think it's a pretty big downside that it's difficult to set up robust replication with sqlite. It's certainly one of the things that cause people to say that it's not a "real" database.