Magento – How to override Mage/Core/Model/Domainpolicy.php in a custom module

I am trying to override

Mage/Core/Model/Domainpolicy.php

Currently I have done it successfully by copying it to:

app/code/local/Mage/Core/Model/Domainpolicy.php

and added my modifications. That works fine.

But instead I would prefer to have it in my own module which is structured as follows:

app/code/local/Me/Mymodule/

and in its config.xml I have:

<?xml version="1.0"?>
<config>
    <modules>
        <Me_Mymodule>
            <version>0.1</version>
        </Me_Mymodule>
    </modules>
    <global>
        <models>
            <core>
                <rewrite>
                    <domainpolicy>Me_Mymodule_Core_Model_Domainpolicy</domainpolicy>
                </rewrite>
            </core>
            <reports_resource>
                <rewrite>
                    <helper_mysql4>Me_Mymodule_Reports_Model_Resource_Helper_Mysql4</helper_mysql4>
                </rewrite>
            </reports_resource>
        </models>
        <blocks>
            <page>
                <rewrite>
                    <html_head>Me_Mymodule_Page_Block_Html_Head</html_head>
                </rewrite>
            </page>
        </blocks>
    </global>
    <frontend>
        <routers>
            <contacts>
                <args>
                    <modules>
                        <Me_Mymodule before="Mage_Contacts">Me_Mymodule_Contacts</Me_Mymodule>
                    </modules>
                </args>
            </contacts>
        </routers>
    </frontend>
</config>

In app/code/local/Me/Mymodule/Core/Model/Domainpolicy.php I have:

class Me_Mymodule_Core_Model_Domainpolicy extends Mage_Core_Model_Domainpolicy

and the original original code with my modifications applied in one of the functions (I just add a few HTTP headers to the original content policy, no any big changes).

The problem is that when I move the modified Domainpolicy.php inside my module and extend the original class as shown (and it is no longer in app/code/local/Mage) Magento doesn't use it but runs the original one (from app/code/core). At the same time all other things which you see I have overriden in the same module work as expected.

What am I missing?