XML : Magento local.xml reference name="header" issue

In a custom theme where the page.xml has been modified with "top.links" block removed from "header":

  <block type="page/html_header" name="header" as="header" />    

I need to reinstate "top.links". So I changed it back to

  <block type="page/html_header" name="header" as="header">      <block type="page/template_links" name="top.links" as="topLinks" />  </block>    

It works.

But when I create a local.xml with the following:

  <default>      <reference name="header">          <block type="page/template_links" name="top.links" as="topLinks"/>      </reference>  </default>    

It doesn't. As a comparison, I tried with the language switcher

  <default>      <reference name="header">          <block type="page/switch" name="store_switcher" as="store_switcher" template="page/switch/stores.phtml"/>      </reference>  </default>    

The language switcher works. But I just can't get the "top.links" working.