Had the same problem, along with some additional graphics anomalies like the the sovereign and units not displaying in portrait windows etc. that disabling advanced lighting fixed.
As far as the cloth map not appearing is concerned I spent some time trying to narrow down which settings being disabled fixed it. It's weired, Advanced lighting needs to be turned off in game then both Smoothvision HD: anisotropic filtering & Smoothvision HD: anti-aliasing need to be switched to use application settings in the ATI control panel. However, once the games loaded with the graphics are all displaying normally, reactivating those overrides in the ATI control panel didn't brake the graphics again (on subsequent loads of the game). So now advanced lighting just needs to stay off. But switching advanced lighting off didn't fix the issue until the ATI control panel settings had been tweaked. :-/
Addendum: After a restart the problem is back. Tweaking 3D settings in the ATI control panel fixes it again most the time... Though it doesn't seem to matter which ones you tweak, or if you set them back to what they originally were again. It's intermittent as well, sometimes it works sometime it doesn't. It's bizarre. I've got the most stable results with Catalyst AI disabled. Enabling then disabling it has consistently worked so far (everything else other then the advanced lighting setting in game is on). I should also add the cloth map is there, it just has a black covering over it. You can see it briefly when alt tabbing, sometimes in full detail sometimes with the black covering only appearing in half of each tile (causing a series of black lines).
