If you parent a camera to an empty (or something else) and use flymode the camera isn't flying. Instead the parent, the empty, is moved/rotated.
I appended a simple example. Just start to rotate the camera in flymode and the empty will start moving, while the camera might react strange, when flying forward/backward.
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Event Timeline
This is intentional, for durian we used a 'Camera Rigs' which needed to have the parent moved rather then the camera.
But its bad for other things, like shaking the camera with an empty (parent). Since you can't move the camera itself, if its constrained by a driver. In this simple scenario you can't fly the camera anymore.
I don't think that this is good in any way if it's not optional.
Do i have to parent the camera to an empty that is parented to an empty with shaking effect?
Ill look into having an option for fly mode and camera locking where you can select between moving the parent or the child.
Added to my todo
http://wiki.blender.org/index.php/User:Ideasman42#TODO
Added a user preference for this, r36824
Interface -> View Manipulation -> Camera Lock Parent