I just thought of something:
Reading the description for the controlBarContent, maybe it's only supposed to work in Panels, and not on the <s:Application> or <s:WindowedApplication> level? Are control bars only meant to be in panels?
Should I go ahead and use an <mx:ControlBar> instead, to display my navigation buttons in the application level?
Window and WindowedApplication do not currently show the controlBarContent, only Panel/TitleWindow/Application do.
See this bug: http://bugs.adobe.com/jira/browse/SDK-23900 and please vote if you would like to see it fixed.
Unfortunately that bug has been closed, even though it hasn't been fixed (weird?). How can we vote for this bug now?
The bug is closed with a "Deferred" resolution. This means that it is closed for now, but might be revisited in a future release of Flex. You should still be able to vote for it and please do. The more votes the better chance it will be reconsidered to be fixed.