in Joomla!, Itemid is important. To test where your site goes, you need to disable SEF and check the Itemid in URL. Because Itemid (id of menu link) mostly determines how the site will look.
One menu link can be displayed different if it uses different Itemid (because you can set different parameters in menu link). With itemid you can differentiate between the home page and other pages.
Mostly, using hidden menu solves all the problems (e.g. because plugins and modules don't have any menu link and they need to get some), see more info: http://www.phoca.cz/documents/16-joomla/338-using-sef-in-joomla
I think, there is not better solution for this.
Jan