Sorry, I should have specified better. By "Linux" I meant the overall mix of Xorg and whatever display or GUI toolkits are in use, and instead of "graphics card", I should have said "graphics card drivers". If the card itself were having issues, I'm sure more than Firefox would have problems. Alternatively, I always hear about how "Linux has bad font rendering!" but since I'm not much of a font guy, I'm not sure if they're referring to how the fonts look, or some deeper part of the process which displays the fonts.
I recently had to switch to the radeon (open source) drivers instead of fglrx (AMD's proprietary) drivers due to some incompatibility with a kernel upgrade. It makes sense that the problem would exist somewhere between Firefox and its use of those drivers.
That does sound like it could easily cause problems. Graphics drivers are bad in all Linux systems. NVIDIA's I've seen tend to work better - just hope Steam does well with Linux and pushes ATI to finally make some good drivers.