I don't know, in all honesty. That behavior obviously doesn't sound correct. Can I get more information and have you try something below: The Logout Redirection URL options are created using a Joomla parameter to show all menus. This should show all menu items (registered or even unpublished). I don't think it shows trashed articles though. Not sure what ones you're seeing, but hopefully that explains a little. It's Joomla's behavior, not ours, but I could see it being confusing.
As for your Home article, can you check to make sure you're using the 'original' Home menu item? If you're using a menu item which is an alias to the real Home, that may cause some problems (though it shouldn't). Additionally, can you try setting the logout to "- Select Item -" and see if it correctly leaves you on the current page (assuming it's not a registered page)? If not, let us know where it tries to take you.
Sorry I don't have a good answer now, but we'll get you fixed up!
Logout redirection
