There is no rule that says you have to and AMD gives you the option to install Catalyst software to any drive you want. Installation for the video card installs required DLL files to windows system directories automatically and that is why it is fine to install the remainder of the catalyst package on your HDD. I questioned this in great detail and AMD video cards will be just as fast even if you choose to install the Catalyst on a different drive. If Catalyst software had to be installed to the root drive, it would not give an option.
I think AMD is smart enough that if any files need to be on the root drive, those files will be put on the root drive while the rest will be stored on the drive and path we selected, and will not cause any difference in video performance at all. I do not know why some people do not want to agree with this. The installation program would probably not give you the option and I am sure if we do have the option and it is not recommended, there is likely going to be a message that states it must be on the root drive. Try to save your SSD for your common executables you use daily that benefit from the speed of your root drive/SSD.