If I remember correctly, DB Classic is based upon DX 7. I thought I read somewhere that they were working on making the ATI 5900 so that it will work with DX 11. Perhaps they weren't too worried about making sure it works with DX 7. (Dunno for sure; just a guess).
TGC has not supported DB Classic for some time, so it's no surprise they want you to go with DB Pro. I doubt that upgrading the ATI drivers will help, but it makes sense to at least suggest that.
The games look like a great deal of work went into the media creation, and perhaps it would be possible to take the DBC source code and make the necessary edits to allow it to run in DB Pro?
BTW, those games look really cool. Are you WRF Studios?