Clarification about MY_Controller and relative inheritances

What is the exact error you get?

I see nothing wrong with your understanding of inheritance. I don't see anything wrong with your code either. I constructed a test case doing the same as you (as I understand it) the test works just fine.

File: application/core/MY_Controller.php

PHP Code:

class MY_Controller extends CI_Controller
{
 function __construct()
 {
 parent::__construct();
 }
}

class Backend extends MY_Controller
{

    public function __construct()
    {
        parent::__construct();
        $this->load->model('rivers_m');
    }

} 


The model is one I had handy that is known to work.

File: application/controllers/Welcome.php

PHP Code:

class Welcome extends Backend
{
    function __construct()
    {
        parent::__construct();
    }

    public function index()
    {
        $data = $this->rivers_m->getRivers();
        var_dump($data);
    } 


The var_dump produces the expected output.