Yeah, it definitely seems to be a (maybe just "almost") coplanar z-fighting issue. Do those lamp shades have "thickness"? Or are they just single faced? (painting on the front and back faces - even if you paint different materials on them - shouldn't cause this problem).
Such a z-fighting can occur with even not entirely coplanar but very close faces like EscapeArtist says. It happens when the "physical" distance of two faces - viewing from far enough - is already foreshortened enough to be less than 1 pixel on screen; the limit OpanGL can display.
In your 2D export that distance must be very very small however (if that's the case) since it's not a very far away shot OR I'd still suggest there are exactly coplanar faces there.