I see people already picking apart what you said, but I see where you're coming from. If course lung cancer is not fake cancer, because it's treated at the same places as other types of cancer. We have hospitals for physical illness though, and you usually see mental illness treated at a separate place. The mental health therapists in my town work out of unremarkable buildings behind some restaurants, while the major hospital has a block to itself with flashy signs identifying what it is. I think that is that leads me to see the "illness" in "mental illness" with a different connotation.