The ATI Radeon card is not supported by the game. Probably because it is too recent. (It does say on the box which graphic chipsets are supported.)
And yes, I would agree with you that in theory Direct3D should be completely hardware independent, but I'm afraid it might not be 100%. On the other hand I think that W&W is probably not as hardware independent as it could be either.
So I think you can blame Heuristic Park for a less than perfect design, Activision for not willing to let HP work on a patch, and perhaps even Microsoft for not completely succeeding in making direct3D hardware independent, and even some graphic cards manufacturers for not being completely Direct3D compatible.
Note that I can't prove any of the above; it's my just opinion.