Unable to reproduce this here. Whether in Network Admin or a sub-blog Admin, the flyouts display properly. The only thing that would have any bearing on this is z-index and I'm only using it on old WP versions on #wphead. It is still a holdover in my recent css files but only in the two that deal with the Toolbar not being displayed. If all other plugins are deactivated, how are you triggering the use of the "No Toolbar" CSS? Please check with Web Developer of similar to see what CSS file is being invoked.
Checking core further, are you doing anything that would use Press This, or trigger colors-classic or colors-fresh to customize your login and admin? There may be a cached CSS file that is causing the conflict; even when the plugin has been deactivated.
I just tried every combination imaginable between AG Custom Admin, Ozh Dropdown, Admin Menus Fixed and standard admin menus and the flyouts work as expected every time. Not sure what else to do.