It turns out if an app:

1) Is running on a platform like Mac that has a system menu bar
2) The app instantiates a MenuBar and then sets the useSystemMenuBarProperty so the MenuBar uses the system menu bar
3) Later instantiates another MenuBar and sets the useSystemMenuBarProperty for this second MenuBar so that the second MenuBar uses the system menu bar
It looks like the setting of the useSystemMenuBarProperty is ignored. It would be good to document that behavior in the javadoc.