No - the way to get the background to look 'right' is to properly illuminate your scene so that it matches the (implied) illumination of your background image. Then, any camera adjustments affect each about equally.
For example, if you have a normally lit scene, but the image file that you choose for a background is underexposed, you'll wash out your scene if you open the lens enough to properly expose the background image. In your original example, it sounds like your scene was not illuminated enough, and so when you ask the camera for a longer exposure (e.g., lower f-stop and/or slower shutter and/or higher ISO speed) to show your scene properly, it then overexposed your background.
With an HDRI background, I assume this wouldn't be an issue ... since in that case, the HDRI image is illuminating the scene and so they are guaranteed to be in the same lighting realm. I haven't played with HDRI much with CR yet... Eduardo and others can give feedback there.
Comparison info on physical renderer (and physical camera) vs standard render:
http://helpcenter.graphisoft.com/guides/archicad-18-int-reference-guide/user-interface-reference/dia...
What kinds of results do you get with your background image with the standard renderer, with global illumination enabled/etc?
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