I think my 2011 TE has a small door as well, but I never close it. Seems more trouble than it's worth and the cords from aux ports always get in the way.
Not the best pics, since it's dark. But you can see what I mean.
Also it doesn't even go all the way down to hide anything. It only hides the plugs and the 2x2 little cubby hole. The bottom space is completely uncovered when it closed.