You are correct.
JSF operates primarily via a series of postback operations done via HTTP POST. For HTTP POST, a form must exist, and to get the extra indicators that help JSF process propertly, it should be a JSF "h:form" or equivalent and not a bare HTML FORM tag with ACTION=POST on it.
This is true even for "hyperlink" tags such as h:commandLink and for menu tags, since, unlike bare HTML A HREF= tags, they will go through the JSF postback engine.