Magento 1 – Fix setTemplate Action Method Not Working

First check if the layout handle is correct.
Add this line in the controller to see the layout handle

echo $this->getFullActionName();

I have a feeling it will print something like this adminhtml_module_sync_index. This is the layout handle you have to use in the layout file.
Also, just to be save, add a name and alias to the block from the content section.
Something like this:

    <adminhtml_module_sync_index><!--put here what you get from the echo in the controller -->
        <reference name="head">
            <action method="setTitle" translate="title">
                <title>Module</title>
            </action>
        </reference>
        <reference name="content">
            <block type="module_sync/adminhtml_index" template="sync/index.phtml" as="index" name="index" />
        </reference>
    </adminhtml_module_sync_index>

You SHould use below code to override methods.phtml

<checkout_onepage_paymentmethod>
        <remove name="right"/>
        <remove name="left"/>

        <block type="checkout/onepage_payment_methods" name="root" output="toHtml" template="codverify/methods.phtml">
            <action method="setMethodFormTemplate"><method>purchaseorder</method><template>payment/form/purchaseorder.phtml</template></action>
        </block>
    </checkout_onepage_paymentmethod>