Inno3d are only working with nvidia. Just like inno3d , palit , zotac and evga, collorfull , PNY point of view. Just like Sapphire, xfx , powercolor sells only only from amd.
The reason they are cheaper is because they work with only one of them and get some exclusivity contracts (cheaper chips). After that each AiB sets its own price depending on how much the invested in it and how much they want to get out of it.
Even though some users have experienced problems with them they aren't necessarily bad. I've heard enough problems plaguing big names like gigabyte (coil noise-bad cooling because they didn't fixed the cooler properly) , asus (dying unexpectedly) or even EVGA's recent burning cards (like literally ,they didn't cooled the vrm , high temps , spontaneous fire ; they fixed it immediately) , so in this regard I'd say nothing is written in stone and simply go with what you can find.