That does't make sense. That's MY video card (I have the 6950 but still).
Do you have a screenshot of what you do see?
One suggestion: There are newer drivers for that card. Mine are substantially newer (I needed them to get KOTOR to work).
will need to wait for darkehound reply on this, cause I have some nonumbered internal intel card. and my drivers are from end of the June. I'm pretty sure they are the current ones.
Two more notes. the game worked correctly in this area around 0.85. it stopped working after the patch, and afterwards when I migrated from win xp to win 7 it continued to be buggy. Secondary I do see the models in unit design, while I don't in other windows. My guess is that it is environment independent and it is not dependant on low level 3d models display code. It is a result of some code checked in, during last 3 months or so, related to UI.
pictures (from 0.951) made just now:
so you could see me logged in:
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346254340.jpg
can't see sovereigns on start new game
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346254347.jpg
but I can see them during sovereing creation
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346254359.jpg
oops, wife called me, laptop autolocked - that's how it look like when you return to the game from locked screen
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256336.jpg
all right, loaded a game, there is a forest drake, let's see him closer on the strategic map, no luck
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256495.jpg
bloody big bastard, no? lets design some new unit to counter him, works ok
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256516.jpg
how about buying some stuff for the champion, noo, don't work
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256540.jpg
oh, I heard you put some funny thing when you reseach a technology yes? no for me
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256725.jpg
and that creatures are now more talkative? I see same creature everytime: 'a big shadow of nothing'
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256921.jpg
so let see this troll from the battlefield, still no luck, just like the drake
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256932.jpg
but I won the battle, and my champion got a level, surprise, surprise, this time I see him plain in his glory
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256959.jpg
finally let's look at the diplo screen, oh, nice touch here, it works 
https://dl.dropbox.com/u/28216465/fe%200.951/FallenEnchantress_1346256995.jpg
that's about all the situation I can think off that the 3d models appear, apart of normal game on the strategic/tactical maps where they work without problems.
ultimately a brand fresh debug.err from the latest crash (I had to run a program with admins priviledges, (you know run as administrator), the screen flipped for a second). when I alt tabbed back to the game it freezed again, so you can confirm the video card specs.
https://dl.dropbox.com/u/28216465/fe%200.951/debug.err