Firstly thank your for your input.
Yes I agree that the composer is the best option for managing and maintaining a php installation, however the package codeigniter/framework is available since 3.0 and we are runing the version 2 so I can not consider this solution.
Now I would like to go to some constructive criticism:
I put here the links for linux regular releases for a reason to not discuss the accuracy of file system hierarchy standards. That's to says you can put the php file where ever you want as far as you follow a correct file permission and ownership approach.
This is an output of phpmyadmin files system installed by debian package manager :
/usr/local# ls -l /usr/share/phpmyadmin/ | grep index
-rw-r--r-- 1 root root 6701 Aug 12 2012 index.php
Here is another output of php files installed by Freebsd package manager:
ls -l /usr/local/share/pear/SOAP/Base.php
-r--r--r-- 1 root wheel 40045 May 15 2009 /usr/local/share/pear/SOAP/Base.php
Should we say that Linux designers have no clue how to manage file system ?
I believe that apache should have read only access to system folders and such folders should be located from /var/www/ so far as possible and this is exactly how the guys from Debian, Ubuntu-Server or Freebsd handle the things.
That is why I think that moving the codeigniter system folder to '/usr/local/codeigniter-version-number/system/' or /usr/local/share/codeigniter-version-number/system/ with root owner ship and 644 file permissions is more accurate than storing it under '/var/www'.