I got it working for my needs. :-)
I don't know how "official" this fix is, but considering Microsoft
documentation about this issue, which is null, I am happy.
First of all, my master is using AspMenu from TopNavBar.ascx, but I think
modifying the menu that is already on the master page should work as well.
(let me know)
My Menu Settings are:
StaticDisplayLevels="1"
and I have these settings for delegatecontrol:
<SharePoint

elegateControl runat="server"
ControlId="TopNavigationDataSource1">
<Template_Controls>
<asp:SiteMapDataSource
ShowStartingNode="false"
SiteMapProvider="GlobalNavSiteMapProvider"
id="topSiteMap"
runat="server"
StartingNodeUrl=""/>
</Template_Controls>
</SharePoint

elegateControl>
Remember to have:
ControlId NOT named as "TopNavigationDataSource"
SiteMapProvider="GlobalNavSiteMapProvider" or
CombinedNavSiteMapProvider" --- right now gives me the same results, but we
will see in the future
StartingNodeUrl="" not sid:1002
The previous menu, which was a drop down menu, had first button named as the
Site title.
That menu item could not be drop down object, so I did not like that.
Actually, having menu item named the same as the Site title was awkward to
me. Some site titles get long names and how to handle that.
With these adjustments, that menu item doesn't show up on my menu bar, which
is more than ok with me.
I hope this works for you, or at least gave you an idea how to adjust your
topNavBar menus.
Of course you will not use these settings for all your menus and sites.
Goran