All GC and Wii games have low resolution textures and are designed to be rendered at 480i/p. Dolphin renders games at 2, 3, or 4x higher resolution, which cleans up the existing textures and makes them look crisper. The textures still have SD levels of detail; it just becomes easier to see the existing details when you render the game in HD and use AA/AF to smooth and sharpen the graphics. All you get with a Wii HDMI adapter is 480p graphics stretched to 720p or 1080p, which doesn't look that good. Rendering the SD graphics in HD is what causes the improvement, and real GC/Wii hardware is not powerful enough to do that.
In order to get truly HD graphics, you must replace the existing SD textures with HD textures that have more detail. Many user created texture packs exist for this purpose, but you have to download them separately.
"Fear the HUnewearl."