The problem, IMO, is in that you are using matrix metering on the white background.
AE camera sensors are set up to expose for an even 50% gray, and do not understand full black or white scenes the way your eye does. If you place something fully white in front of a camera, it will under expose to grey. If you place a full black sheet in front of a camera, it will over-expose to gray. They are set up this way because most scenes that you look at have a more dynamic set of luminance values than your studio setup.
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