So if I have no databases that start with "-", I'm not vulnerable? Didn't quite understand what they meant by that.
Just from the quote cited by octo_t I would read that you are still vulnerable: A malicious database user could craft a _connection string_ which contains a database name starting with -. There's no hint that the database has to exist on your server for this to work, so I would read it could be a complete bogus request and still damage your files.
PQconnectdb("host=127.0.0.1 dbname=-exploit user=postgres password=postgres port=5432");