In VDL-DOC, there is this description about @ajaxRendered:
Defines, whether the content of this component must be (or not) included in AJAX response created by parent AJAX Container, even if it is not forced by reRender list of ajax action. Ignored if component marked to output by some Ajax action component. Default value - "true"
This comes from AjaxOutputProps. The description is valid for other components (probably), but not for a4j:outputPanel, because the default value is overridden in AbstractOutputPanel with the opposite value.