I am sorry to disagree but, IMHO, this is not a bug but the way it works. And I am not sure if it could work differently, or if it would be better than now. That’s why it has not been reported as a bug 
First, in Blender, IPOs are just function curves. Any animated parameter uses IPOs: bones, objects, textures, anything. The matter here is if the animation is stored in an Action or at the general timeline, called the NLA (non-linear-animation) window in Blender. Also, Armature animations are the only ones you can use Actions for, and you cannot animate bones outside Actions.
So if you want to have an Armature animated with an action, and then also animated as an object (transforms), you will first build an Action and then add the transform animation for the Armature Object at the NLA timeline, where you can also mix and match several Actions, playing with their influences, duration and so on.
The fbx exporter was developed specifically for Unity, and his main purpose is getting Armature animations inside Unity (object animations can be easily done inside Unity itself, and are often managed by the game logic and/or physics). And one of the benefits is you get each Action as a separate animation in Unity automatically. No need to painfully separate them again in Unity, no need to build up a lot of different files, each with a different animation. The perfect workflow.
But what if you want to animate some Objects in Blender? Well, you can still do it using the NLA window, but for this not to collide with the Armatures-Actions workflow, you must first indicate you want to use the NLA data (the exporter option “Current Action”) instead of exporting the Actions as takes. If the objects you are animating are Armatures with Actions, then what you get exported this way are the baked bones animations, but re-edited with the NLA tools. No need to export the original Actions, as it would be redundant and you can have some Actions not used at the NLA. And how can the exporter know if you want the first or the last option when Unity launches it automatically? It simply cannot.
I have seen other exporters trying to resolve this issue too, as the DTS exporter for Torque, and I think the current solution is the best one. The last version of the mentioned exporter switched form the Actions-as-takes approach to the “Export the NLA animation” way, and I frankly think it is worst now, making me stay with the old version.
My 2 cents.