Need to install mysql in php webserver to access remote server mysql database?

Need to install mysql in php webserver to access remote server mysql
database?

I'm trying to setup an separate debian webserver using php-fpm and nginx
to access remote mysql server. So far after I go through several setup
from this reference
http://www.cyberciti.biz/tips/how-do-i-enable-remote-access-to-mysql-database-server.html
After finish, it works when I remote it from outside using command line
mysql -uxxx -p -hxxxxx
Then when I try it on my web server using fuelphp to access the database,
it give me error:
Fuel\Core\Database_Exception [ 2002 ]: Can't connect to local MySQL server
through socket '/var/run/mysqld/mysqld.sock' (2)
It seems try to find socket locally to connect to the remote mysql. On the
installation of php, I already include apt-get php5-mysql and others
except mysql server.
My question: is it possible to setup webserver without have to install
mysql in the local machine in order to access mysql on remote? I want to
optimize the webserver by separating it from the database. Thanks