Ok, I was able to recreate this on My Windows XP SP3 machine (core2duo) that has an ATI 4870 running Cat 11.7 (1 version behind). I tried running in different compatibility modes but that didn't do anything. I also treid manipulating a few of the driver settings for the card but that didn't work either.
I use this machine primarily for work so I really don't want to go swapping in and out different video boards to figure out if it's an ATI driver issue, but I'll upgrade to Cat 11.8 and see if we get lucky. I'll update this post to let you know.
*UPDATE: 11.8 has the same issue. Was hoping against hope we'd get lucky. At this point I don't know what to suggest...maybe run it in software mode on the levels where this occurs? I know that sucks but I don't know where else to take this. You could also build an older machine. I don't know where the problem lies but I can tell you Win 98 with an Nvidia ti4200 doesn't have this issue. If I'd have to guess I'd say it's modern ATI drivers. Can't guarantee that modern Nvidia drivers don't do this as well though. Sorry man if I think of anything else I'll get back to you.