When using Canon paper on a Canon printer, you set the printer driver "media type" setting so it's the same as the paper. But when you use a 3rd party paper, you still have to set the media type to a Canon paper rather than the exact paper you're using. This feels a lot like using the wrong profile.
Then in the printing application (at least in Elements or DPP) you set the profile of your paper. So what exactly does the driver's media type setting do, and how does it interact with the profile setting in the printing application?